Question

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

Answer 1

Foci are at `(0, +-sqrt3)`. 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 and e = sqrt(1-b^2/a^2)=sqrt3,`

The foci are at `(0, +-sqrt3)`

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]}