SOLUTION: Find the equation of the outer edge of the elliptical pool table shown below. Assume the red ball is at the focus. Here is the picture: http://imgur.com/a/qGevT

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the equation of the outer edge of the elliptical pool table shown below. Assume the red ball is at the focus. Here is the picture: http://imgur.com/a/qGevT       Log On


   

Question 915212: Find the equation of the outer edge of the elliptical pool table shown below. Assume the red ball is at the focus.
Here is the picture: http://imgur.com/a/qGevT

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
If the pool table is longest at 60in, then your a=60%2F2=30, and if it is widest at 40in, then b=40%2F2=20
The equation for an ellipse at the origin is:
x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1+
And plugging in:
x%5E2%2F%2830%29%5E2%2By%5E2%2F%2820%29%5E2=1+
x%5E2%2F900%2By%5E2%2F400=1+
That is your equation.
The foci are given as the points of distance c from the center, where:
a%5E2=b%5E2%2Bc%5E2+
So solving for "c%7D%7D%22+yields%3A%0D%0A%0D%0A%7B%7B%7B30%5E2-20%5E2=c%5E2+
900-400=c%5E2+
500=c%5E2
sqrt%28500%29=c+

22.36=c+ or -22.36=c+
The foci are at (-22.36,0) and (22.36,0)
vertices: (-30,0) and (30,0)
center: (0,0)