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Question

The circle with major axis as diameter is called the auxiliary circle of the hyperbola.
If a>b, then the equation of auxiliary circle is

A
x2+y2=a2
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B
x2+y2=b2
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C
x2+y2=a2b2
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D
x2+y2=a2+b2
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Solution

The correct option is B x2+y2=a2
For any Hyperbola of the form x2a2y2b2=1

Length of Major axis is always 2a, though a can be greater, lesser or equal to b

For any conjugate Hyperbola x2a2y2b2=1 or y2b2x2a2=1

The length of major axis is always 2b, Though b can be greater, lesser or equal to a

So For any Hyperbola the circle drawn taken major axis as a diameter also called auxiliary circle of the Hyperbola will have a diameter of 2a, equal to the length of major axis and center same as center of Hyperbola.

Hence equation of Auxiliary circle of any Hyperbola will be x2+y2=a2

So the correct option is A

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