Question

Answer the following:

Find the equation of the tangent to the hyperbola `x^2/25 − y^2/16` = 1 at P(30°)

Answer 1

The equation of the hyperbola is `x^2/25 − y^2/16` = 1

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

a² = 25, b² = 16

∴ a = 5, b = 4

The equation of the tangent to the hyperbola

`x^2/"a"^2 - y^2/"b"^2` = 1 at P(θ) is

`x/"a"sectheta - y/"b"tantheta` = 1

∴ the equation of the tangent to the given hyperbola at P (30°) is

`x/5sec30^circ - y/4tan30^circ` = 1

∴ `x/5(2/sqrt(3)) - y/4(1/sqrt(3))` = 1

∴ 8x – 5y = `20sqrt(3)`