Whats an equation for the ellipse that has a foci of 02and02

What\'s an equation for the ellipse that has a foci of (0,2)and(0,-2) and vertices of (0,5)and (0,-5)

Solution

center is midway between the two foci, so (h, k) = ( 0, (-2+2)/2 ) = ( 0, 0)

vertices are 5 units from centre : a =5

Each focus is 2 units from the center, so c = 2.

b^2 = a^2 - c^2 = 25 - 4 = 21

So, x^2/25 + y^2/21 = 1 ( equation for the ellipse )