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}/a^{2}+ (y-k)^{2}/b^{2}= 1 where h and k are the x and y co-ordinates of the center point which is (0,0). Simplifying: x^{2}/a^{2 }+^{ }y^{2}/b^{2}= 1. Also, "a" equals the length from the center of the ellipse to the vertex which, in this case, is 5, and c^{2}= a^{2}- b^{2 }. Substituting c^{2}= 1^{2}, or 1,^{ }and a^{2}= 5^{2}, or 25, we get: 1 = 25-b^{2}, or b^{2}= 25-1, or b^{2}= 24. With a

^{2 }= 25, b^{2}= 24 the equation of this ellipse can be written as x

^{2}/25 + y^{2}/24 = 1