Question

The equation of tangent at a point with eccentric angle $\theta$ to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

• A. $\frac{x}{a}\sec \theta -\frac{y}{b}\tan \theta =1$
• B. $\frac{x}{a}\cot \theta +\frac{y}{b}\sec \theta =1$
• C. $\frac{x}{a}\tan \theta -\frac{y}{b}\sec \theta =1$

Answer 1

The correct option is A $\frac{x}{a}\sec \theta -\frac{y}{b}\tan \theta =1$

The parametric equation of tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is

$\frac{x}{a}\sec \theta -\frac{y}{b}\tan \theta =1$.