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

77x - 21y - 265 = 0

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21x - 77y + 265 = 0

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21x - 77y - 265 = 0

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21x + 77y - 265 = 0

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Solution

The correct option is D 21x + 77y - 265 = 0
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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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

The correct option is D 21x + 77y - 265 = 0ransverse axis is the equation of the angle bisector passing containing point (2, 3), which is given by 3x−4y+55=12x+5y−4013 ⇒ 21x+77y=265

The correct option is D 21x + 77y - 265 = 0
ransverse axis is the equation of the angle bisector passing containing point (2, 3), which is given by
$\frac{3 x - 4 y + 5}{5} = \frac{12 x + 5 y - 40}{13}$
$\Rightarrow$ $21 x + 77 y = 265$