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