Question

The eccentricity of the conic $4(2y-x-3{)}^2-9(2x+y-1{)}^2=80$ is

• A. $\frac{\sqrt{15}}{2}$
• B. $\frac{\sqrt{13}}{3}$
• C. $\frac{\sqrt{13}}{2}$
• D. $\frac{\sqrt{15}}{3}$

Answer 1

The correct option is B $\frac{\sqrt{13}}{3}$

Let $2y-x-3=X$ and $2x+y-1=Y$
Here, $X$ and $Y$ are perpendicular lines.
Equation of conic will be $4X^2-9Y^2=80$
$\Rightarrow \frac{X^2}{\frac{80}{4}}-\frac{Y^2}{\frac{80}{9}}=1$
$e^2=1+\frac{b^2}{a^2}=1+\frac{80}{9\times \frac{80}{4}}=1+\frac{4}{9}=\frac{13}{9}$
$\therefore$ $e=\frac{\sqrt{13}}{3}$