Show that `x^2+4y^2-2x+16 y+13=0` is the equation of an ellipse. Find its eccentricity.

Explanation

`(x^{2}+2 xright)+4(y^{2}+4 yright)+13=0`


`Rightarrow(x^{2}+2 x+1right)+4(y^{2}+4 y+4right)=4`


`Rightarrow(x+1)^{2}+4(y+2)^{2}=4`


`Rightarrow frac{(x+2)^{2}}{4}+frac{(y+2)^{2}}{1}=1`


Hence eccentricity `=sqrt{1-frac{1}{4}}=frac{sqrt{3}}{2}`