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The locus of mid- point of chord of parabola $${ y }^{ 2 }=4ax$$ which touches the parabola $${ x }^{ 2 }=4by$$ is :

A

$$\left( 2ax-{ y }^{ 2 } \right) ={ 4a }^{ 2 }b$$

B

$$y\left( 2ax+{ y }^{ 2 } \right) ={ 4a }^{ 2 }b$$

C

$$y\left( 2ax-{ y }^{ 2 } \right) ={ a }^{ 2 }b$$

D

$$y\left( 2ax-{ y }^{ 2 } \right) ={ 4a }^{ 2 }b$$

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Solution

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Correct option is D. $$y\left( 2ax-{ y }^{ 2 } \right) ={ 4a }^{ 2 }b$$

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