Find the equation of an ellipse whose foci are (0,±6) and whose semi-minor axis is 5

Question

Find the equation of an ellipse whose foci are (0,±6) and whose semi-minor axis is 5

Answer 1

Foci are given as (0,+-c) = (0,+-6), so:

Major axis is vertical so vertices are (0,+-a)

Minor axis is horizontal so co-vertices are (+-b, 0) = (+-5,0)

a^2 + b^2 = c^2

a^2 + 25 = 36

a^2 = 11

equation of ellipse with major axis vertical is:

x^2/b^2 + y^2/a^2 = 1

since b^2 = 25 and a^2 = 11

x^2/25 + y^2/11 = 1