Question

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

• \[77x-21y-265=0\]

• \[21x-77y+265=0\]

• \[21x-77y-265=0\]

• \[21x+77y-265=0\]

Answer 1

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 \[21x+77y-265=0\].

Explanation:

Transverse axis is the equation of the angle bisector containing point (2, 3)0 which is given by 

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

\[\Rightarrow\quad13(3x-4y+5)=5(12x+5y-40)\]

\[\Rightarrow\quad21x+77y=265\]