Question

Find the equation of the tangent to the hyperbola: x = 3 sec θ, y = 5 tan θ at θ = π/3

Answer 1

Given, equation of the hyperbola is x = 3 sec θ, y = 5 tan θ 

Since sec² θ – tan² θ = 1,

\(\frac {x^2}{9} - \frac {y^2}{25} = 1\)

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

we get 

a² = 9 and b² = 25 

a = 3 and b = 5 

Equation of tangent at P(θ) is

10x – 3√3 y = 15