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From the points on the circle x^(2)+y^(2...

From the points on the circle `x^(2)+y^(2)=a^(2)`, tangents are drawn to the hyperbola `x^(2)-y^(2)=a^(2)`: prove that the locus of the middle-points `(x^(2)-y^(2))^(2)=a^(2)(x^(2)+y^(2))`

A

`(x^(2)-y^(2))^(2)=a^(2)(x^(2)+y^(2))`

B

`(x^(2)-y^(2))=2a^(2)(x^(2)+y^(2))`

C

`(x^(2)-y^(2))^(2)=a^(2)(x^(2)-y^(2))`

D

`2(x^(2)-y^(2))^(2)=3a^(2)(x^2 +y^2)`

Text Solution

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The correct Answer is:
C
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