Question

Find the equations of the tangents to the hyperbola x²/25 - y²/9 = 1 making equal intercepts on the co-ordinate axes.

Answer 1

Given equation of the hyperbola is \(\frac {x^2}{25} - \frac {y^2}{9} = 1\)

Comparing this equation with \(\frac {x^2}{a^2} - \frac {y^2}{b^2} = 1\)

we get 

a² = 25, b² = 9

Since the tangents make equal intercepts on the co-ordinate axes, 

∴ m = -1 

Equations of tangents to the hyperbola \(\frac {x^2}{a^2} - \frac {y^2}{b^2} = 1\) having slope m are

⇒ y = -x ± √16 

⇒ x + y = ±4