Chords of the hyperbola x^(2)-y^(2)=a^(2...

Chords of the hyperbola `x^(2)-y^(2)=a^(2)` touch the parabola `y^(2)=4ax`. Prove that the locus of their middle-points is the curve `y^(2)(x-a)=x^(3)`.

A

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

B

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

C

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

D

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

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The correct Answer is:

B

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