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If the transverse axis is $3 x + 4 y = 7$
Conjugate axis is $4 x + 8 = 3 y$
Transverse axis length = 4
Conjugate axis length = 6
Then the equation of hyperbola is

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$\frac{{(4 x - 3 y + 8)}^{2}}{100} - \frac{{(3 x + 4 y - 7)}^{2}}{225} = 1$

$\frac{{(4 x - 3 y + 8)}^{2}}{100} + \frac{{(3 x + 4 y - 7)}^{2}}{225} = 1$

$\frac{{(4 x - 3 y + 8)}^{2}}{225} - \frac{{(3 x + 4 y - 7)}^{2}}{100} = 1$

$\frac{{(4 x - 3 y + 8)}^{2}}{225} + \frac{{(3 x + 4 y - 7)}^{2}}{100} = 1$

answer is A.

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Detailed Solution

$p u t X = \frac{4 x - 3 y + 8}{5}, Y = \frac{3 x + 4 y - 7}{5}$

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