The normal at a variable point on an ellipse of eccentricity meets the axes of the…

MATHEMATICS · Single correct · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane

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 (1)

e'

is independent of

e

(2)

e' = 1

(3)

e' = e

(4)

e' = \frac{1}{e}