Question

The eccentricity of the ellipse represented by the equation $25x^2+16y^2-150x-175=0$ is

• A. $2/5$
• B. $3/5$
• C. $4/5$
• D. None of these

Answer 1

Answer: (B)

The given equation is
$25\left(x^2-6x\right)+16\left(y^2\right)=175$
$\Rightarrow 25{\left(x-3\right)}^2+16{\left(y-0\right)}^2=400$
$\Rightarrow \frac{{\left(x-3\right)}^2}{16}+\frac{\left(y-0\right)}{25}=1$
The major axis of this ellipse is a line parallel to the $y$-axis i.e. $x=3$. Therefore, its eccentricity is given by
$e=\sqrt{1-\frac{a^2}{b^2}}=\sqrt{1-\frac{16}{25}}=\frac{3}{5}\cdot$