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

77 x - 21 y - 265 = 0

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21 x - 77 y + 265 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

21 x - 77 y - 265 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

21 x + 77 y - 265 = 0

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Solution

The correct option is D $21 x + 77 y - 265 = 0$
Transverse axis is the equation of the angle bisector of the asymptotes given by
$\frac{3 x - 4 y + 5}{\sqrt{3^{2} + 4^{2}}} = \frac{12 x + 5 y - 40}{\sqrt{(12)^{2} + 5^{2}}}$
$\frac{3 x - 4 y + 5}{5} = \frac{12 x + 5 y - 40}{13}$
$\Rightarrow 21 x + 77 y = 265$

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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=0Transverse axis is the equation of the angle bisector of the asymptotes given by 3x−4y+5√32+42=12x+5y−40√(12)2+523x−4y+55=12x+5y−4013⇒21x+77y=265

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