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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


Question ID - 57162 | Toppr 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

1 Answer - 5876 Votes

3537

Answer Key : (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.



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