Question

Find the standard form equation for each ellipse described.

1) Major vertices at (0, 3) and (0, -3), minor vertices at (2, 0) and (-2, 0)

2) Major vertices at (7, 0) and (-7, 0), foci at (5, 0) and (-5, 0)

3) Minor vertices at (-2, -3) and (-2, -11), foci at (1, -7) and (-5, -7)

Answer 1

I'll do a freebie for you. Maybe you can attempt the rest and show your work.

The major semi-axis half the distance between the major vertices. Similarly for minor.

#1:
maj semi = 3
min semi = 2
x^2/4 + y^2/9 = 1

#3 is similar, but the center has been translated. Recall that the center at (h,k) means

(x-h)^2/a^2 + (y-k)^2/b^2 = 1