# How do you find the foci and sketch the ellipse x^2+1/4y^2=1?

Jan 14, 2017

Foci are at $\left(0 , \pm \sqrt{3}\right)$. See foci-marked graph,.

#### Explanation:

The equation is in the standard form

${x}^{2} / {b}^{2} + {y}^{2} / {a}^{2} = 1.$

The center is O. Major axis is aling y-axis.

$a = 2 , b = 1 \mathmr{and} e = \sqrt{1 - {b}^{2} / {a}^{2}} = \sqrt{3} ,$

The foci are at $\left(0 , \pm \sqrt{3}\right)$

graph{xy(x^2+y^2/4-1)(x^2+(y+1.732)^2-0.004)(x^2+(y-1.732)^2-0.004)(y-1.732)(y+1.732)=0 [-5, 5, -2.5, 2.5]}