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Exercise 11.3 - Chapter 11 Conic Sections class 11 ncert solutions Maths - SaraNextGen [2024]


Question 1:

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5443/chapter%2011_html_44e3930c.gif

Answer:

The given equation ishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5443/chapter%2011_html_44e3930c.gif .

Here, the denominator of https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5443/chapter%2011_html_86db3.gif is greater than the denominator ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5443/chapter%2011_html_5d4ada9a.gif .

Therefore, the major axis is along the x-axis, while the minor axis is along the y-axis.

On comparing the given equation withhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5443/chapter%2011_html_m64d080ba.gif , we obtain = 6 and b = 4.

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5443/chapter%2011_html_2c5a2d4c.gif

Therefore,

The coordinates of the foci arehttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5443/chapter%2011_html_m578ee8b6.gif .

The coordinates of the vertices are (6, 0) and (–6, 0).

Length of major axis = 2a = 12

Length of minor axis = 2b = 8

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5443/chapter%2011_html_m2b5bc57.gif

Length of latus rectum https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5443/chapter%2011_html_m76de02aa.gif

Question 2:

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5444/chapter%2011_html_10a4843f.gif

Answer:

The given equation ishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5444/chapter%2011_html_m74596571.gif .

Here, the denominator of https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5444/chapter%2011_html_2c2847ad.gif is greater than the denominator ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5444/chapter%2011_html_6d70d3c8.gif .

Therefore, the major axis is along the y-axis, while the minor axis is along the x-axis.

On comparing the given equation withhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5444/chapter%2011_html_m4d428e43.gif , we obtain = 2 and a = 5.

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5444/chapter%2011_html_m123b0d3a.gif

Therefore,

The coordinates of the foci arehttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5444/chapter%2011_html_6065d9f0.gif .

The coordinates of the vertices are (0, 5) and (0, –5)

Length of major axis = 2a = 10

Length of minor axis = 2b = 4

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5444/chapter%2011_html_29949993.gif

Length of latus rectum https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5444/chapter%2011_html_45386b26.gif

Question 3:

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5445/chapter%2011_html_b40375c.gif

Answer:

The given equation ishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5445/chapter%2011_html_18135d87.gif .

Here, the denominator of https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5445/chapter%2011_html_9f5a351.gif is greater than the denominator ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5445/chapter%2011_html_m3668c715.gif .

Therefore, the major axis is along the x-axis, while the minor axis is along the y-axis.

On comparing the given equation withhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5445/chapter%2011_html_m64d080ba.gif , we obtain = 4 and b = 3.

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5445/chapter%2011_html_2c16e717.gif

Therefore,

The coordinates of the foci arehttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5445/chapter%2011_html_m53b00781.gif .

The coordinates of the vertices arehttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5445/chapter%2011_html_686926ab.gif .

Length of major axis = 2a = 8

Length of minor axis = 2b = 6

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5445/chapter%2011_html_m68a90d39.gif

Length of latus rectum https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5445/chapter%2011_html_3818a1a6.gif

Question 4:

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5446/chapter%2011_html_m1a8440c4.gif

Answer:

The given equation ishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5446/chapter%2011_html_m1fde515.gif .

Here, the denominator of https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5446/chapter%2011_html_m3a0b37d5.gif is greater than the denominator ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5446/chapter%2011_html_27cf422a.gif .

Therefore, the major axis is along the y-axis, while the minor axis is along the x-axis.

On comparing the given equation withhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5446/chapter%2011_html_m4d428e43.gif , we obtain = 5 and a = 10.

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5446/chapter%2011_html_m68f80cee.gif

Therefore,

The coordinates of the foci arehttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5446/chapter%2011_html_68df6116.gif .

The coordinates of the vertices are (0, ±10).

Length of major axis = 2a = 20

Length of minor axis = 2b = 10

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5446/chapter%2011_html_m39be10d1.gif

Length of latus rectum https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5446/chapter%2011_html_m4f49d33f.gif

Question 5:

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5447/chapter%2011_html_50332c76.gif

Answer:

The given equation ishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5447/chapter%2011_html_m3e91ef85.gif .

Here, the denominator of https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5447/chapter%2011_html_m265f42b7.gif is greater than the denominator ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5447/chapter%2011_html_m2f4628be.gif .

Therefore, the major axis is along the x-axis, while the minor axis is along the y-axis.

On comparing the given equation withhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5447/chapter%2011_html_m64d080ba.gif , we obtain = 7 and b = 6.

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5447/chapter%2011_html_234dc835.gif

Therefore,

The coordinates of the foci arehttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5447/chapter%2011_html_m2b5a897e.gif .

The coordinates of the vertices are (± 7, 0).

Length of major axis = 2a = 14

Length of minor axis = 2b = 12

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5447/chapter%2011_html_2d5f65b0.gif

Length of latus rectumhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5447/chapter%2011_html_62479d1e.gif

Question 6:

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5448/chapter%2011_html_5983e98d.gif

Answer:

The given equation ishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5448/chapter%2011_html_m26bb6d42.gif .

Here, the denominator of https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5448/chapter%2011_html_446b35d9.gif is greater than the denominator ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5448/chapter%2011_html_fce83d.gif .

Therefore, the major axis is along the y-axis, while the minor axis is along the x-axis.

On comparing the given equation withhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5448/chapter%2011_html_m4d428e43.gif , we obtain = 10 and a = 20.

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5448/chapter%2011_html_7ec749ac.gif

Therefore,

The coordinates of the foci arehttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5448/chapter%2011_html_m3fb3a3e4.gif .

The coordinates of the vertices are (0, ±20)

Length of major axis = 2a = 40

Length of minor axis = 2b = 20

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5448/chapter%2011_html_7889be10.gif

Length of latus rectumhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5448/chapter%2011_html_m2d25d1d9.gif

Question 7:

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 36x2 + 4y2 = 144

Answer:

The given equation is 36x2 + 4y2 = 144.

It can be written as

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5449/chapter%2011_html_1e69b416.gif

Here, the denominator of https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5449/chapter%2011_html_69710dc1.gif is greater than the denominator ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5449/chapter%2011_html_m57101b8d.gif .

Therefore, the major axis is along the y-axis, while the minor axis is along the x-axis.

On comparing equation (1) withhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5449/chapter%2011_html_m4d428e43.gif , we obtain = 2 and a = 6.

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5449/chapter%2011_html_m153541ab.gif

Therefore,

The coordinates of the foci arehttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5449/chapter%2011_html_m31ce93e4.gif .

The coordinates of the vertices are (0, ±6).

Length of major axis = 2= 12

Length of minor axis = 2b = 4

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5449/chapter%2011_html_m56527a1b.gif

Length of latus rectum https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5449/chapter%2011_html_5d41d0a0.gif

Question 8:

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 16x2 + y2 = 16

Answer:

The given equation is 16x2 + y2 = 16.

It can be written as

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5450/chapter%2011_html_mfdf949d.gif

Here, the denominator of https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5450/chapter%2011_html_1355c9ae.gif is greater than the denominator ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5450/chapter%2011_html_78195c51.gif .

Therefore, the major axis is along the y-axis, while the minor axis is along the x-axis.

On comparing equation (1) withhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5450/chapter%2011_html_m4d428e43.gif , we obtain = 1 and a = 4.

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5450/chapter%2011_html_m497b97f2.gif

Therefore,

The coordinates of the foci arehttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5450/chapter%2011_html_m44c45a02.gif .

The coordinates of the vertices are (0, ±4).

Length of major axis = 2a = 8

Length of minor axis = 2b = 2

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5450/chapter%2011_html_5ec1d73d.gif

Length of latus rectumhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5450/chapter%2011_html_4a0fc915.gif

Question 9:

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 4x2 + 9y2 = 36

Answer:

The given equation is 4x2 + 9y2 = 36.

It can be written as

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5451/chapter%2011_html_m6f85a24e.gif

Here, the denominator of https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5451/chapter%2011_html_m5c172c6f.gif is greater than the denominator ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5451/chapter%2011_html_12025d58.gif .

Therefore, the major axis is along the x-axis, while the minor axis is along the y-axis.

On comparing the given equation withhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5451/chapter%2011_html_m64d080ba.gif , we obtain = 3 and b = 2.

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5451/chapter%2011_html_73f2d960.gif

Therefore,

The coordinates of the foci arehttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5451/chapter%2011_html_mf509437.gif .

The coordinates of the vertices are (±3, 0).

Length of major axis = 2a = 6

Length of minor axis = 2b = 4

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5451/chapter%2011_html_m3938b939.gif

Length of latus rectumhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5451/chapter%2011_html_m7f673582.gif

Question 10:

Find the equation for the ellipse that satisfies the given conditions: Vertices (±5, 0), foci (±4, 0)

Answer:

Vertices (±5, 0), foci (±4, 0)

Here, the vertices are on the x-axis.

Therefore, the equation of the ellipse will be of the formhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5452/chapter%2011_html_m64d080ba.gif , where is the semi-major axis.

Accordingly, a = 5 and c = 4.

It is known thathttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5452/chapter%2011_html_m3286f72c.gif .

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5452/chapter%2011_html_530eb685.gif

Thus, the equation of the ellipse ishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5452/chapter%2011_html_361f5bc2.gif .

Question 11:

Find the equation for the ellipse that satisfies the given conditions: Vertices (0, ±13), foci (0, ±5)

Answer:

Vertices (0, ±13), foci (0, ±5)

Here, the vertices are on the y-axis.

Therefore, the equation of the ellipse will be of the formhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5453/chapter%2011_html_m4d428e43.gif , where is the semi-major axis.

Accordingly, a = 13 and c = 5.

It is known thathttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5453/chapter%2011_html_m3286f72c.gif .

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5453/chapter%2011_html_1f1643e0.gif

Thus, the equation of the ellipse ishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5453/chapter%2011_html_m7a10013.gif .

Question 12:

Find the equation for the ellipse that satisfies the given conditions: Vertices (±6, 0), foci (±4, 0)

Answer:

Vertices (±6, 0), foci (±4, 0)

Here, the vertices are on the x-axis.

Therefore, the equation of the ellipse will be of the formhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5454/chapter%2011_html_m64d080ba.gif , where is the semi-major axis.

Accordingly, a = 6, c = 4.

It is known thathttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5454/chapter%2011_html_m3286f72c.gif .

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5454/chapter%2011_html_m76a9ffa1.gif

Thus, the equation of the ellipse ishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5454/chapter%2011_html_m6d188d9d.gif .

Question 13:

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis (±3, 0), ends of minor axis (0, ±2)

Answer:

Ends of major axis (±3, 0), ends of minor axis (0, ±2)

Here, the major axis is along the x-axis.

Therefore, the equation of the ellipse will be of the formhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5455/chapter%2011_html_m64d080ba.gif , where is the semi-major axis.

Accordingly, a = 3 and b = 2.

Thus, the equation of the ellipse ishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5455/chapter%2011_html_m73a0b10d.gif .

Question 14:

Find the equation for the ellipse that satisfies the given conditions: Ends of major axishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5456/chapter%2011_html_m716c9d36.gif , ends of minor axis (±1, 0)

Answer:

Ends of major axishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5456/chapter%2011_html_m716c9d36.gif , ends of minor axis (±1, 0)

Here, the major axis is along the y-axis.

Therefore, the equation of the ellipse will be of the formhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5456/chapter%2011_html_m4d428e43.gif , where is the semi-major axis.

Accordingly, a =https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5456/chapter%2011_html_52caafc6.gif  and b = 1.

Thus, the equation of the ellipse ishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5456/chapter%2011_html_m73e00e5a.gif .

Question 15:

Find the equation for the ellipse that satisfies the given conditions: Length of major axis 26, foci (±5, 0)

Answer:

Length of major axis = 26; foci = (±5, 0).

Since the foci are on the x-axis, the major axis is along the x-axis.

Therefore, the equation of the ellipse will be of the formhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5457/chapter%2011_html_m64d080ba.gif , where is the semi-major axis.

Accordingly, 2a = 26 ⇒ a = 13 and c = 5.

It is known thathttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5457/chapter%2011_html_m3286f72c.gif .

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5457/chapter%2011_html_1f1643e0.gif

Thus, the equation of the ellipse ishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5457/chapter%2011_html_2e3e969d.gif .

Question 16:

Find the equation for the ellipse that satisfies the given conditions: Length of minor axis 16, foci (0, ±6)

Answer:

Length of minor axis = 16; foci = (0, ±6).

Since the foci are on the y-axis, the major axis is along the y-axis.

Therefore, the equation of the ellipse will be of the formhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5458/chapter%2011_html_m4d428e43.gif , where is the semi-major axis.

Accordingly, 2b = 16 ⇒ b = 8 and c = 6.

It is known thathttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5458/chapter%2011_html_m3286f72c.gif .

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5458/chapter%2011_html_m5bfd9fd4.gif

Thus, the equation of the ellipse ishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5458/chapter%2011_html_246d9d7b.gif .

Question 17:

Find the equation for the ellipse that satisfies the given conditions: Foci (±3, 0), a = 4

Answer:

Foci (±3, 0), a = 4

Since the foci are on the x-axis, the major axis is along the x-axis.

Therefore, the equation of the ellipse will be of the formhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5459/chapter%2011_html_m64d080ba.gif , where is the semi-major axis.

Accordingly, c = 3 and a = 4.

It is known thathttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5459/chapter%2011_html_m3286f72c.gif .

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5459/chapter%2011_html_68aa1337.gif

Thus, the equation of the ellipse ishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5459/chapter%2011_html_5effa4cf.gif .

Question 18:

Find the equation for the ellipse that satisfies the given conditions: b = 3, c = 4, centre at the origin; foci on the axis.

Answer:

It is given that b = 3, c = 4, centre at the origin; foci on the axis.

Since the foci are on the x-axis, the major axis is along the x-axis.

Therefore, the equation of the ellipse will be of the formhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5460/chapter%2011_html_m64d080ba.gif , where is the semi-major axis.

Accordingly, b = 3, c = 4.

It is known thathttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5460/chapter%2011_html_m3286f72c.gif .

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5460/chapter%2011_html_66038583.gif

Thus, the equation of the ellipse ishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5460/chapter%2011_html_361f5bc2.gif .

Question 19:

Find the equation for the ellipse that satisfies the given conditions: Centre at (0, 0), major axis on the y-axis and passes through the points (3, 2) and (1, 6).

Answer:

Since the centre is at (0, 0) and the major axis is on the y-axis, the equation of the ellipse will be of the form

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5461/chapter%2011_html_m5d4fb08b.gif

The ellipse passes through points (3, 2) and (1, 6). Hence,

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5461/chapter%2011_html_aea257e.gif

On solving equations (2) and (3), we obtain b2 = 10 and a2 = 40.

Thus, the equation of the ellipse ishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5461/chapter%2011_html_7808e979.gif .

Question 20:

Find the equation for the ellipse that satisfies the given conditions: Major axis on the x-axis and passes through the points (4, 3) and (6, 2).

Answer:

Since the major axis is on the x-axis, the equation of the ellipse will be of the form

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5462/chapter%2011_html_m3c832535.gif

The ellipse passes through points (4, 3) and (6, 2). Hence,

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5462/chapter%2011_html_m59b2810a.gif

On solving equations (2) and (3), we obtain a2 = 52 and b2 = 13.

Thus, the equation of the ellipse ishttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/5462/chapter%2011_html_4eddb78.gif .

Also Read : Exercise-11.4-Chapter-11-Conic-Sections-class-11-ncert-solutions-Maths

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