Eliminate 0 from the following : x = 3 , y = 4 - Vidyadip

Question

Eliminate 0 from the following $: x = 3\sec \theta, y = 4 \tan \theta$

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Answer

$x=3 \sec \theta, y=4 \tan \theta$
$\therefore \sec \theta=\frac{x}{3}$ and $\tan \theta=\frac{y}{4}$
We know that,
$\sec ^2 \theta-\tan ^2 \theta=1$
$\therefore \quad\left(\frac{x}{3}\right)^2-\left(\frac{y}{4}\right)^2=1$
$\therefore \quad \frac{x^2}{9}-\frac{y^2}{16}=1$
$\therefore 16 x^2-9 y^2=144 $

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