# Find the corresponding rectangular equation represented by the parameteric equations; x=1+sec theta and y=2 + tan theta by eliminating the parameter.

Find the corresponding rectangular equation represented by the parameteric equations; by eliminating the parameter.
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Luna Wells
it can be written as $x-1=\mathrm{sec}\theta$...(1)
$y-2=\mathrm{tan}\theta$...(2)
squaring on both sides eqns (1) and (2)and subtracting
$\left(x-1{\right)}^{2}-\left(y-2{\right)}^{2}={\mathrm{sec}}^{2}\theta -{\mathrm{tan}}^{2}\theta$

$⇒{x}^{2}-{y}^{2}-2x-4y-4=0$