SOLUTION: Find the standard form of the equation of the ellipse with the given characteristics? Foci: (0, 0) and (4, 0) Major Axis of length 8

Algebra ->  Finance -> SOLUTION: Find the standard form of the equation of the ellipse with the given characteristics? Foci: (0, 0) and (4, 0) Major Axis of length 8      Log On


   

Question 1116896: Find the standard form of the equation of the ellipse with the given characteristics?

Foci: (0, 0) and (4, 0)
Major Axis of length 8
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) The foci are on the major axis, equidistant from the center of the ellipse. So the center of the ellipse is (2,0).

(2) Major axis in the x direction with center (2,0) makes the standard form of the equation %28x-2%29%5E2%2Fa%5E2%2B%28y-0%29%5E2%2Fb%5E2+=+1

(3) Major axis length 8 makes a=4.

(4) Distance from center to each focus is c=2, where c^2 = a^2-b^2. With c^2=4 and a^2=16, b^2=12.

The equation in standard form is %28x-2%29%5E2%2F16%2B%28y%29%5E2%2F12+=+1