Question

In parametric representation of a standard hyperbola in $\theta$ terms, if $x=asec\theta$. What is y.

• A. $bcosec\theta$
• B. $btan\theta$
• C. $bcos\theta$
• D. $bsin\theta$

Answer 1

The correct option is B

$btan\theta$

A parametric form of any curve would be something which would be satisfied in the standard form.If we put the parametric values in the equation $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ it would satisfy.This would help us deriving such parametric form in some non standard cases.

Here let $y_1$ be the parametric form

$\frac{a^{2}se{c}^2\theta }{a^2}+\frac{y_1^2}{b^2}=1$

$\frac{y_1^2}{b^2}=1-se{c}^2\theta$

=$ta{n}^2\theta$

$y_1=btan\theta$