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A normal to the hperbola `(X^(2))/(a^(2))-(y^(2))/(b^(2))=1` meets the axes at M and N and lines MP and NP are drawn perpendicular to the axes meeting at P. Prove that the locus of P is the hyperbola `a^(2)x^(2)-b^(2)y^(2)=(a^(2)+b^(2))^(2)`.

A

e' is eccentricity of conjugate of `(x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1`

B

`(1)/(e^(2)) + (1)/(e^(2)) =1`

C

`e^(2) + e'^(2) =3`

D

`e^(2) + e'^(2) =4`

Text Solution

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The correct Answer is:
A, B
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