Equation of a rectangular hyperbola whose asymptotes are $x = 3$ and $y = 5$ and passing through $(7, 8)$ is

x y - 3 y + 5 x + 3 = 0

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x y + 3 y + 4 x + 3 = 0

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x y - 3 y + 5 x - 3 = 0

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x y - 3 y - 5 x + 3 = 0

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Solution

The correct option is D $x y - 3 y - 5 x + 3 = 0$
The equation of rectangular hyperbola is
$(x - 3) (y - 5) + λ = 0$
Since, it passes through $(7, 8) .$
$\Rightarrow λ = - 12$
$∴ x y - 5 x - 3 y + 15 - 12 = 0$
$\Rightarrow x y - 3 y - 5 x + 3 = 0$ is the required equation of rectangular hyperbola.

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