The equation of the circle having one of its diameter as end points of foci of x2a2+y2b2=1(a>b), is
A
x2+y2=a2+b2
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B
x2+y2=a2
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C
x2+y2=2a2
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D
x2+y2=a2−b2
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Solution
The correct option is Dx2+y2=a2−b2 Coordinates of focii of the ellipse x2a2+y2b2=1 are (±ae,0)
So centre of required circle is (0,0) with radius ae units.
Hence, the equation of the circle is x2+y2=a2e2 ⇒x2+y2=a2(1−b2a2) ⇒x2+y2=a2−b2