Question

Write an equation of the ellipse with foci (+-4,0) and co-vertices at (0,+-2)

Answer 1

@iGreen

Answer 2

One step at a time.

It's an ellipse. It looks like this:

\(\dfrac{x^{2}}{}+\dfrac{y^{2}}{} = 1\)

co-vertices at (0,+-2) -- This is the y-direction, so...

\(\dfrac{x^{2}}{}+\dfrac{y^{2}}{2^{2}} = 1\)

foci (+-4,0) -- This is the x-direction, as it should be. What do we know about the relationship of vertices (a), co-vertices (b) and foci (c) for an ellipse? b^2 + c^2 = a^2

How do we find that pesky 'a'?