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