SOLUTION: Find the equation of the ellipse with the center at the origin. Latus rectum 4, distance between foci 4sqrt(2). I dont know of im doing it right. Here's my progress. p = 4/2

Click here to see ALL problems on Quadratic-relations-and-conic-sections

Question 957784: Find the equation of the ellipse with the center at the origin.
Latus rectum 4, distance between foci 4sqrt(2).
I dont know of im doing it right. Here's my progress.
p = 4/2 = 2
c = 4sqrt(2)/2 = 2sqrt(2)
p = b^2/a
2 = b^2/a
b^2 = 2a
c^2 = a^2 - b^2
b^2 = a^2 - c^2
b^2 = a^2 - 8
p a = a^2 - c^2
Am I doing it the right way to solve for a?
Answer by Edwin McCravy(20060) (Show Source):
You can put this solution on YOUR website!

In the graph above, the green line is the latus rectum, the two red points are the foci. The distance between the foci is given as Since c is half the distance between foci, . Since the latus rectum is given as 4, the y-coordinate of the point at the top of the latus rectum is 2. So the coordinates of the point at the top of the latus rectum are . The equation of the ellipse is (1) Substituting that point: (2) Since and Substituting in (2) That has solutions a=4, a=-4, a=2, a=-2 The only one it can be is a=4 Substituting in So the equation of the ellipse, substituting in (1), Edwin