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The locus of the mid-points of the chord...

The locus of the mid-points of the chords of the circle `x^(2) + y^(2) = 16` which are the tangents to the hyperbola `9x^(2) - 16y^(2) = 144` is

A

`12 x ^(2) - 8y ^(2) = x ^(2) + y ^(2)`

B

`9x ^(2) + 12 y ^(2) = (x ^(2) + y ^(2)) ^(2)`

C

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

D

`16x ^(2) -6y ^(2) =x ^(4) + y ^(4)`

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The correct Answer is:
C
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