Prove that the limiting points of the system x^2 + y^2 + 2gx + c + (x^2 + y^2 + 2fx +…

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

Problem

Prove that the limiting points of the system

x^2 + y^2 + 2gx + c + \lambda(x^2 + y^2 + 2fx + k) = 0

subtend a right angle at the origin, if

\frac{c}{g^2} + \frac{k}{f^2} = 2