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If normal at P to a hyperbola of eccentricity e intersects its transverse and conjugate axes at L and M, respectively, then prove that the locus of midpoint of LM is a hyperbola. Find the eccentricity of this hyperbola

A

`e_1=(e )/(e^2-1)`

B

`e_1=sqrt((e )/(e^2-1))`

C

`e_1=(e )/(sqrt(e^2-1))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
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VMC MODULES ENGLISH-CONIC SECTIONS-LEVEL - 2
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