Prove that the straight line is a normal to the ellipse if a^2 l^2 + b^2 m^2 = (a^2 -…

MATHEMATICS · Subjective · ISC · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

Prove that the straight line

lx + my + n = 0

is a normal to the ellipse

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

\frac{a^2}{l^2} + \frac{b^2}{m^2} = \frac{(a^2 - b^2)^2}{n^2}.