Find the vertices of the ellipse centered at the origin with eccentricity e=13 and foci at (0,−2) and (0,2).

Answer 1

Eccentricity of an ellipse is the number e = c/a

In this problem c = 2 (distance between center and focus), e = 13

So a = 2/13

This gives the vertices on the x axis (2/13, 0) and (0, 2/13)

To get the vertices on the y axis we need b

Use the equation c^2 = b^2 - a^2 with c = 2 and a = 2/13 to solve for b

(Note that c^2 = a^2 - b^2 will end up giving an imaginary value for c which is not allowed.)

b = 4.61(approx)

So the vertices on the y axis are (0, 4.61), (0, - 4.61)