need to find the equation of an ellipse
Because the center of the ellipse is at the origin and a focus is on the x-axis the foci can be written as (c,0) and (-c,0). Therefore c=1 and the major axis is on the x-axis which means the standard form of this ellipse will be in this form: (x-h)2/a2 + (y-k)2/b2 = 1 where h and k are the x and y co-ordinates of the center point which is (0,0). Simplifying: x2/a2 + y2/b2 = 1. Also, "a" equals the length from the center of the ellipse to the vertex which, in this case, is 5, and c2 = a2 - b2 . Substituting c2 = 12, or 1, and a2 = 52, or 25, we get: 1 = 25-b2, or b2 = 25-1, or b2 = 24.
With a2 = 25, b2 = 24 the equation of this ellipse can be written as
x2/25 + y2/24 = 1