If we are given the equation of an ellipse in geometric form, how do we find the foci?

Answer 1

Algebraically, an ellipse is x^2/a^1 + y^2/b^2 = 1 if centered at the origin

the focus is (c,0) and (-c,0) where c^2 =a^2 - b^2 if a>b

geometrically, look at the vertices, the top and right most points

(0,b) and (a,0) if a>b then (c,0) and (-c,0) are the focus points

if b>a, then (0,c) and (0,-c) are the focus points with c^2=b^2-a^2