Question

Eccentricity of the hyperbola whose asymptotes are given by $3x+2y+5=0$ and $2x+3y+5=0$ is

• A. $\sqrt{2}$
• B. $\frac{3}{2}$
• C. $2$
• D. None of these

Answer 1

Answer: (A)

$\sqrt{2}$

$\begin{array}{cc}3x+2y+5=0& 2x+3y+5=0\\ 3x+2y=-5& -3y=2x-5\\ 2y=-3x-5& y=\frac{-2}{\left(-3\right)}x-\frac{5}{\left(-3\right)}\\ y=\frac{-3}{2}x-\frac{5}{2}& y=\frac{2}{3}x+\frac{5}{3}\\ m=\frac{-3}{2}\times \frac{2}{3}=-1& \end{array}$

It is a rectangle

$\therefore e=\sqrt{2}$