If a hyperbola passes through (2, 3) and has asymptotes 3x

Question

If a hyperbola passes through (2, 3) and has asymptotes 3x - 4y + 5 = 0 and 12x + 5y - 40 = 0, then the equation of its transverse axis is

Options:

A . 77x - 21y - 265 = 0

B . 21x - 77y + 265 = 0

C . 21x - 77y - 265 = 0

D . 21x + 77y - 265 = 0

Answer: Option D
:
D
ransverse axis is the equation of the angle bisector passing containing point (2, 3), which is given by

\frac{3 x - 4 y + 5}{5} = \frac{12 x + 5 y - 40}{13}

\Rightarrow

21 x + 77 y = 265

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