The Ellipse. Thank you!

Question

Give the equation in standard form of the ellipse centered at the origin with a focus at , and a vertex at .

Answer 1

equation of ellipse is x^2/b^2 + y^2/a^2 = 1

vertices are (0,+/-a), so if vertex is (0,6), then a is 6 and a^2 is 36.

foci are (0, +/- c), so if focus is (0,3), then c is 3

c^2 = a^2 - b^2

9 = 36 - b^2

b^2 = 27

so equation is x^2/27 + y^/36 = 1