Prove that the straight lines and always meet on a hyperbola.

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Prove that the straight lines

\frac{x}{a} - \frac{y}{b} = m

and

\frac{x}{a} + \frac{y}{b} = \frac{1}{m}

always meet on a hyperbola.