Prove that the point lies on the hyperbola for all values of ( ).

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

Problem

Prove that the point

\left\{ \frac{a}{2} \left( t + \frac{1}{t} \right), \frac{b}{2} \left( t - \frac{1}{t} \right) \right\}

lies on the hyperbola for all values of

t

(

t \neq 0