Answer
$\frac{(y-4)^2}{9}-\frac{(x-2)^2}{9}=1$
Work Step by Step
We know that $\tan^2 A+1=\sec^2 A$. $\tan t=\frac{x-2}{3},\sec t=\frac{y-4}{3}$
Hence here $(\frac{x-2}{3})^2+1=(\frac{y-4}{3})^2$, thus $\frac{(y-4)^2}{9}-\frac{(x-2)^2}{9}=1$
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