Find the equation of an ellipse satisfying:

Question

Find the equation of an ellipse satisfying: Foci at (2,2) and (6,2) and major axis ending at the point (10,2). Express this equation in standard form.

Answer 1

Mateo,

 

The standard formula of a ellipse is (x-h)^2/a^2+(y-k)^2/b^2=1 where h,k is the center of the ellipse. Since the foci is (2,2) and (6,2), we know the center is (4,2) making h=4 and k=2. The major axis ends at (10,2), meaning the far right vertice occurs at (h+a,k) making a=6. The far right foci occurs at (h+c,k) making c=2. By definition a^2-b^2=c^2 so

36-b^2=4 and b^2=32

 

Now we have (x-4)^2/36+(y-2)^2/32=1

 

Hope that helps!