Find an equation for the ellipse that satisfies the given conditions.

Question

Length of major axis: 26, foci on x-axis, ellipse passes through the point (square root of 13, 6) centered at the origin

Answer 1

x^2/13^2 + y^2/b^2 = 1

13/13^2 + 36/b^2 = 1

1/13 + 36/b^2 = 1

36/b^2 = 1-1/13 = 12/13

3/b^2 = 1/13

b^2 = 39

x^2/169 + y^2/39 = 1

or

(x^2)/13 + (y^2)/3 = 13

it might help to sketch the graph

major axis vertices are (-a,0), (a,0) = (-13,0), (13,0)

and minor axis verticies are (0,-b) (0, b) = (0, -3sqr(13/3)) (0, 3sqr(13/3)) = about (0, -6.245), (0, 6.245)

foci are (sqr(a^2-b^2), 0) = (-sqr130, 0), (sqr130, 0) = about (-11.402, 0) (11.402)