Question

For an ellipse, one focus is (0,0), one vertex is (2,0), and the eccentricity is 0.4. How do I find the equation for the ellipse? It seems like I have so little information!

Answer 1

x^2/a^2 + y^2/b^2 = 1 is the standard equation , and eccentricity=sqrt(1-b^2/a^2)

Here the equation is..

second point.
4/a^2=1 a=2

first point:
.4=sqrt(1-b^2/4)
.16=1-b^2/4
.64=4-b^2
b^2=3.36

x^2/4 + y^2/3.36=1

check all that work

Answer 2

I get it now! However, I think you made a mistake with .16=1-b^2/4. It should be turned into .64=1-b^2, and then b^2=0.36. Then x^2/4 + y^2/0.36=1.