Question

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

Answer 1

The ellipse passes through `(±2, 0)` and `(0, ±1/2)`.
It's laying `(a > b)` then the foci are on `x` axis, aren't they?

Explanation:

`x^2 / a^2 + y^2 / b^2 = 1 ; a = 2 ; b = 1/2`

When `y = 0`, `x^2 = 4 Rightarrow x = ± 2`

When `x = 0`, `4y^2 = 1 Rightarrow y = ± 1/2`

`a^2 + b^2 = c^2`

`c = sqrt{4 + 1/4} = sqrt 17 / 2`

I don't remember whether the foci are `(±c, 0)` or `(0, ±c)`