Question

The eccentricity of the ellipse $x^2+4y^2+8y-2x+1=0$ is

• A. $\frac{\sqrt{3}}{2}$
• B. $\frac{\sqrt{5}}{2}$
• C. $\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

The correct option is A $\frac{\sqrt{3}}{2}$

Given ellipse
$x^2+4y^2+8y-2x+1=0$
$1x^2+4y^2+8y-2x+1=0\Rightarrow (x^2-2x+1)+(4y^2+2.2y.2+4)-4=0$
$\Rightarrow \frac{{(x-1)}^2}{4}+\frac{{(y+1)}^2}{1}=1$ is the ellipse
$\therefore a^2=4,b^2=1$
also $b^2=a^2(1-e^2)\Rightarrow e^2=1-\frac{1}{4}=\frac{3}{4}$
$\Rightarrow e=\frac{\sqrt{3}}{2}$