A normal to the hyperbola meets the axes in and and lines and are drawn…

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

Problem

A normal to the hyperbola

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

meets the axes in

M

and

N

and lines

MP

and

NP

are drawn perpendiculars to the axes meeting at

P

. Prove that the locus of

P

is the hyperbola

a^2 x^2 - b^2 y^2 = (a^2 + b^2)^2.