Question

Find the equation of the tangent to the hyperbola: x²/144 - y²/25 = 1 at the point whose eccentric angle is π/3

Answer 1

Given equation of the hyperbola is x²/144 - y²/25 = 1 

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

We get 

a² = 144 and b² = 25

∴ a = 12 and b = 5

Equation of the tangent to the hyperbola \(\frac {x^2}{a^2} - \frac {y^2}{b^2} = 1\) at P (θ) is 

 

∴ 5x - 6√3y = 30