Question

Eliminate $\theta$ ,if
(i) $x=asec\theta ,y=b\tan \theta$

Answer 1

$$\begin{gathered} \mathrm{Given}:x=asec\theta \Rightarrow sec\theta =\frac{x}{a} \\ \mathrm{and}y=b\tan \theta \Rightarrow \tan \theta =\frac{y}{b} \\ \mathrm{We}\mathrm{know}\mathrm{that}se{c}^2\theta -{\tan }^2\theta =1 \\ \Rightarrow {\left({\displaystyle \frac{x}{a}}\right)}^2-{\left(\frac{y}{b}\right)}^2=1 \\ \therefore \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \end{gathered}$$