Find the equation of the ellipse with the following properties.
the ellipse with x-intercepts (5, 0) and (-5, 0); y-intercepts (0, 3) and (0, -3).

Equation of an ellipse:

(x-h)²/a² + (y-k)²/b² = 1
Since it passes through the origin (0,0) , then h = k = 0 hence the equation:
(x-0)²/a² + (y-0)²/b² = 1
x²/a² + y²/b² = 1

2a = major axis = 2.|5| + |-5| = 10. then a = 5 and a² = 25
2b = minor axis = 2.|3| + |-3| = 6. then b = 3 and b² = 9

Then the final equation is:
x²/25 + y²/9 = 1