Prove that the line will be a normal to the hyperbola if a^2 l^2 - b^2 m^2 = (a^2 +…

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Prove that the line

lx + my - n = 0

will be a normal to the hyperbola

\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}.