Find an equation of the ellipse that has center (3, 3), a minor axis of length 4, and a vertex at (3, -1).

Answer 1

minor axis = 4

major axis = 2(3--1) = 2(4) = 8

center = (3,3)

(x-3)^2/2^2 + (y-3)^2/4^2 = 1

(x-3)^2/4 + (y-3)^2/16 = 1

it may help to plot the points and sketch a rough graph of the ellipse

with vertices (3,-1), (3,7), (5,3) and (1,3)

check the solution by plugging in those points

or, eliminating fractions the ellipse is:

4x^2-24x +y^2 -6y +29 = 0