Mathematics

Mathematics

Problem

The normal at a variable point

P

on an ellipse

\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1

of eccentricity

e

meets the axes of the ellipse in

Q

and

R

, then the locus of the mid-point of

QR

is a conic with eccentricity

e'

such that a.

e'

is independent of

e

b.

e' = 1

c.

e' = e

d.

e' = \frac{1}{e}

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