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Question

The equation of auxillary circle is x225y216=1

A
x2+y2=16
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B
x2+y2=32
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C
x2+y2=25
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D
x2+y2=41
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Solution

The correct option is D x2+y2=25
For any Hyperbola of the form x2a2y2b2=1,

The circle drawn taken major axis as a diameter also called the 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 standard Hyperbola will be x2+y2=a2

Here the given hyperbola is x225y216=1, which is similar to standard form of the hyperbola.

Here a=5 and b=4

The equation of Auxiliary circle for the given hyperbola will also be x2+y2=(5)2

x2+y2=25

So the correct option is C

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