Eliminate 0 from the following : x = 3 – 4 ,3y = 5 + 3

Question

Eliminate 0 from the following $: x = 3 – 4 \tan \theta,3y = 5 + 3\sec \theta$

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Answer

$2 x=3-4 \tan \theta \text { and } 3 y=5+3 \sec \theta$
$\therefore 2 x-3=-4 \tan \theta \text { and } 3 y-5=3 \sec \theta$
$\therefore \tan \theta=\frac{3-2 x}{4} \text { and } \sec \theta=\frac{3 y-5}{3} \theta$
We know that, $\sec ^2 \theta-\tan ^2 \theta=1$
$\therefore\left(\frac{3 y-5}{3}\right)^2-\left(\frac{3-2 x}{4}\right)^2=1$
$\therefore\left(\frac{3 y-5}{3}\right)^2-\left(\frac{2 x-3}{4}\right)^2=1 $

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