Question

Find the equations of the tangents to the hyperbola `x^2/25 - y^2/9` = 1 making equal intercepts on the co-ordinate axes

Answer 1

Given equation of the hyperbola is `x^2/25 - y^2/9` = 1.

Comparing this equation with `x^2/"a"^2 - y^2/"b"^2` = 1, we get

a² = 25 and b² = 9

Since the tangents make equal intercepts on the co-ordinate axes, m = – 1.

Equations of tangents to the hyperbola

`x^2/"a"^2 - y^2/"b"^2` = 1 having slope m are

y = `"m"x ± sqrt("a"^2"m"^2 - "b"^2)`

∴ y = `-x ± sqrt(25(-1)^2 - 9)`

∴ y = `-x ± sqrt(16)`

∴ x + y = ± 4.