A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the centre of this circle, is
a.
A hyperbola
b.
A parabola
c.
A straight line
d.
An ellipse
a.
A hyperbola
b.
A parabola
c.
A straight line
d.
An ellipse
Question ID - 57162 | SaraNextGen Top Answer A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the centre of this circle, is
a.
A hyperbola
b.
A parabola
c.
A straight line
d.
An ellipse
A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the centre of this circle, is
|
a. |
A hyperbola |
b. |
A parabola |
|
c. |
A straight line |
d. |
An ellipse |
1 Answer
127 votes
Answer Key / Explanation : (b) -
Let equation of circle is
x2 + y2 + 2fx + 2fy + e = 0, it passes through (0, 2b)
⇒ 0 + 4b2 + 2g × 0 + 4f + c = 0
⇒ 4b2 + 4f + c = 0 ...(i)
2
= 4a ….(ii)
g2 − c = 4a2
⇒ c = (g2 − 4a2)
Putting in equation (1)
⇒ 4b2 + 4f + g2 − 4a2 = 0
⇒ x2+4y+4(b2 − a2) = 0, it represent a parabola.
127 votes
Answer Link
127