Graphing Ellipses

Question

Find the vertices of the ellipse centered at the origin with eccentricity e=1/5 and focus at (-4,0) and (4,0). 

 

(Enter each solution as an ordered pair.)

Answer 1

Eccentricity e = c/a

 

Since the center is (0,0) and the foci are (4,0) and (-4,0),

 

    c = distance from the center to a focus = 4

 

So, e = 4/a = 1/5.  Therefore, a = 20

 

In an ellipse, c² = a² - b²

 

                   16 = 400 - b²     b² = 384

 

Equation of ellipse:  x²/400 + y²/384 = 1