Find an equation of the ellipse satisfying the given conditions.

Question

Center at (-2,3) with major axis of length 8 and parallel to the y axis, minor axis of length 2.
I don't understand how you get the formula for this. some help please

Answer 1

you should know that an ellipse with center at (h,k) and axes 2a,2b is

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

so, plug in your data. The only tricky part is knowing which are a and b. Since the major axis is parallel to the y-axis, (y-k)^2/b^2 will have the larger denominator.

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