Find the equation of the ellipse with center (-3,-2), a focus at (-3,1), and a vertex at (-3,3).
What do I do first?
Sorry, I just realized that you don't have a point on the ellipse. Instead you will have to use trig to find b.
You have a focus (-3,1). The definition of a focus is that the distance from the two focus' to any point on the ellipse is constant.
Eg. If you have point A and point B on the ellipse, the distance from f1 to A to f2 will be the same as f1 to B to f2. Am I explaining this clearly?
Since your one focus is (-3,1), your other will be (-3, -5). The distance from one focus to the vertex given, to the second focus is 10. Since the two focuses are equidistant from each other, the point b is therefore 5 away from both focuses. Use Pythagoras to solve for b in this manner: