Prove that the straight line lx + my + n = 0 touches the ellipse x^2 a^2 + y^2 b^2 =…

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

Problem

Prove that the straight line

lx + my + n = 0 \text{ touches the ellipse } \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \text{ if } a^2l^2 + b^2m^2 = n^2.