Question

A hyperbola of the form $\frac{(x-h{)}^2}{a^2}-\frac{(y-k{)}^2}{b^2}=1$ can be parametrically represented as $(asec\theta +h,btan\theta +k)$

• A. True
• B. False

Answer 1

The correct option is A

True

This is the easy way of arriving at the parametric equation.

We are making use of the identity

$se{c}^2\theta -ta{n}^2\theta =1$

Comparing this with the equation of the given hyperbolas

$\frac{x-h}{a}=sec\theta and\frac{y-k}{b}=tan\theta$

$x=(asec\theta +h)y=btan\theta +k$

$\therefore$ Required parametric form= $(asec\theta +h,btan\theta +k)$