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A tangent to the hyperbola (x^2)/(a^2)-(...

A tangent to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` cuts the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` at `Pa n dQ` . Show that the locus of the midpoint of `P Q` is `((x^2)/(a^2)+(y^2)/(b^2))^2=(x^2)/(a^2)-(y^2)/(b^2)dot`

A

`((x^(2))/(a^(2)))^(2)+((y^(2))/(b^(2)))^(2)=1`

B

`((x^(2))/(a^(2)))^(2)-((y^(2))/(b^(2)))^(2)=1`

C

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

D

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

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