ellipses conic sections

Question

this ellipse is centered at the origin find the equation

vertices: (-4,0) and (4,0)

foci: (-3,0) and (3,0)

Answer 1

The general equation (with no offsets) is x²/a² + y²/b² = 1

We are told that the foci are at x = -3 and +3, and the vertices are at x = -4 and +4. This is therefore a "horizontal ellipse", with a = 4 and f = 3

We know that a line from the focus to the top or bottom must be = to a. Thus a² = f² + b²

Solving for b, we have b² = (a² - f²) = (16 - 9) = 7

So the equation is x²/16 + y²/7 = 1