Question

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).

Answer 1

x^2/25 + y^2/9 = 1

Explanation:

a = 5, b = 3, center = (0,0). Since 2a lies horizontally, a^2 goes under x^2 of the equation. Since the center is (0,0), leave alone x^2 and b^2 and put a^2 which is 25 under x^2 and put b^2 which is 9 under y^2. So the final equation is x^2/25 + y^2/9 = 1

Answer 2

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