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Question

The equation of the circle drawn with the two foci of x2a2+y2b2=1 as the end-points of a diameter is
(a) x2 + y2 = a2 + b2
(b) x2 + y2 = a2
(c) x2 + y2 = 2a2
(d) x2 + y2 = a2 − b2

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Solution

(d) x2+y2=a2-b2We have r=aeLet the equation of the circle be x2+y2=r2.Now, x2+y2=a2e2 r=ae x2+y2=a21-b2a2 e=1-b2a2x2+y2=a2-b2 The required equation of the circle is x2+y2=a2-b2.

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