SOLUTION: How do i find the equation of an ellipse with the vertex at (0,-10) and the co-vertex at (6,0)? The center is (0,0).

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: How do i find the equation of an ellipse with the vertex at (0,-10) and the co-vertex at (6,0)? The center is (0,0).      Log On


   

Question 920729: How do i find the equation of an ellipse with the vertex at (0,-10) and the co-vertex at (6,0)? The center is (0,0).
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2By%5E2=R%5E2<--->x%5E2%2FR%5E2%2By%5E2%2FR%5E2=1 is the equation of a circle of radius R centered at (0,0).
Since x%5E2%3C=x%5E2%2By%5E2=R%5E2 , x%5E2%3C=R%5E2 and -R%3C=x%3C=R .
Similarly, since y%5E2%3C=x%5E2%2By%5E2=R%5E2 , y%5E2%3C=R%5E2 and -R%3C=y%3C=R .
An ellipse is just a circle stretched more in one direction than the other.
In your case, you will have vertices at (0,-10) and (0,10),
meaning that -10%3C=y%3C=10 ,
and co-vertices at (-6,0) and (6,0),
meaning that -6%3C=x%3C=6 .
A circle with radius 6 would have the equation x%5E2%2F6%5E2%2By%5E2%2F6%5E2=1 ,
and all its points would have to comply with
-6%3C=x%3C=6 and -6%3C=y%3C=6 .
We want -6%3C=x%3C=6 for the x coordinates,
but -10%3C=y%3C=10 for the y coordinates,
so the equation for the ellipse is
x%5E2%2F6%5E2%2By%5E2%2F10%5E2=1 .