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The equation of the transverse axis of the hyperbola ${(x - 3)}^{2} + {(y + 1)}^{2} = {(4 x + 3 y)}^{2}$ is

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$4 x + 3 y = 9$

$4 x + 3 y = 0$

$3 x - 4 y = 13$

$x + 3 y = 0$

answer is C.

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Detailed Solution

${(x - 3)}^{2} + {(y + 1)}^{2} = {(4 x + 3 y)}^{2}$ or ${(x - 3)}^{2} + {(y + 1)}^{2} = 25 {(\frac{4 x + 3 y}{5})}^{2}$

PS=5PM
Therefore, the directrix is $4 x + 3 y = 0$ and the focus is $(3, - 1) .$
So, the equation of transverse axis is
$y + 1 = \frac{3}{4} (x - 3)$ Or, $3 x - 4 y = 13$

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