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Q.
The equation of a rectangular hyperbola whose asymptotes are $x=3$ and $y=5$ and passing through $(7,8)$ is
Conic Sections
Solution:
The equation of the rectangular hyperbola is
$(x-3)(y-5)+\lambda=0$
It passes through $(7,8)$. Hence,
$ 4 \times 3+\lambda $ or $ \lambda=-12$
$\therefore x y-5 x-3 y+15-12=0$
or $ x y-3 y-5 x+3=0$