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The locus of the midpoints of the chord ...

The locus of the midpoints of the chord of the circle, `x ^(2) + y ^(2) = 25` which is tangent to the hyperbola, `(x ^(2))/( 9) - (y ^(2))/(16)=1` is :

A

`(x^(2) +y^(2))^(2)- 9x^(2)-16y^(2)= 0`

B

`(x^(2) +y^(2))^(2) - 9x^(2) + 144y^(2)= 0`

C

`(x^(2) +y^(2))^(2)- 16x^(2) + 9y^(2)= 0`

D

`(x^(2) +y^(2))^(2)- 9x^(2) + 16y^(2)= 0`

Text Solution

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The correct Answer is:
D
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