Question

Given a generic equation for a parabola or an ellipse such as \(y=ax^2+bx+c\) or \(\frac{y^2}{a^2}+\frac{x^2}{b^2}=c^2\), how do you find the focus/foci?

Answer 1

I guess the one for the ellipse should rather be just \(\frac{y^2}{a^2}+\frac{x^2}{b^2}=1\).

Answer 2

For the ellipse, foci are:

If a > b
F1(c;0) and F2(-c;0)
where c² = a² - b²

If a < b
F1(0;c) and F2(0;-c)
where c² = b² - a²