SOLUTION: how do i find the foci of an ellipse? the longer part of the ellipse is at (1,0) and (-3,0) while the shorter part is (-1,1) and (-1,-1)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: how do i find the foci of an ellipse? the longer part of the ellipse is at (1,0) and (-3,0) while the shorter part is (-1,1) and (-1,-1)      Log On


   

Question 884161: how do i find the foci of an ellipse? the longer part of the ellipse is at (1,0) and (-3,0) while the shorter part is (-1,1) and (-1,-1)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Your long part tells the distance between main vertices. This is 4, so a=4%2F2=2.

Your short part tells about b. b=1.

The important relationship to know for an ellipse is b%5E2%2Bc%5E2=a%5E2. Understand that c is the distance from the center of the ellipse to either focus.
c%5E2=a%5E2-b%5E2
c%5E2=2%5E2-1%5E2
c%5E2=4-1
c=sqrt%283%29

To find either focus, you want to know the center.
Your given points allow you to observe or calculate center is at (-1,0).

Foci: ( sqrt%283%29-1,0 ) and ( -sqrt%283%29-1, 0 )