Question

The equation of the hyperbola whose asymptotes are the straight lines 3x – 4y + 7 = 0 and 4x + 3y + 1 = 0 and which passes through the origin, is

• A.
• B.
• C.
• D. None of the above

Answer 1

The correct option is A

The combined equation of the asymptotes is
(3x -4y + 7)(4x + 3y + 1) = 0
So, the combined equation of the hyperbola is
$(3x-4y+7)(4x+3y+1)+\lambda =0$
It passes through the origin.
$\therefore$ $7\times 1+\lambda =0\Rightarrow \lambda =-7$
On putting the value of \lambda in equation (i), we get
(3x - 4y + 7)(4x + 3y + 1) - 7 = 0
$\Rightarrow 12x^2-7xy-12y^2+31x+17y=0$, which is the equation of the required hyperbola