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

Mar 14, 2017

The ellipse passes through (±2, 0) and (0, ±1/2).
It's laying $\left(a > b\right)$ 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

${a}^{2} + {b}^{2} = {c}^{2}$

$c = \sqrt{4 + \frac{1}{4}} = \frac{\sqrt{17}}{2}$

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