Because the sum of the distances from one point on the ellipse to the two focal points is 10, 2a= 10, and a=5.

Because there is an a 2 = b 2+c 2 on the ellipse, b = sqrt (a 2-b 2) = 4.

So the equation is x 2/25+y 2/16 =1or y 2/25+x 2/16 =1.

Where sqrt is the root and 2 is the square.