Find the center, vertices, and foci of the ellipse with equation 5x² + 9y² = 45.

Solution:

The given equation of the ellipse is

5x² + 9y² = 45

Dividing the equation by 45

x²/9 +  y²/5 = 1

Here the center is (0, 0)

Vertices = (±a, 0) = (±3, 0)

a² = b² + c² 

Substituting the values

c² = 9 - 5 = 4

c = 2

Foci = (±c, 0) = (±2, 0)

Therefore, the center, vertices, and foci of the ellipse are (0, 0), (±3, 0) and (±2, 0).

Find the center, vertices, and foci of the ellipse with equation 5x² + 9y² = 45.

Summary:

The center, vertices, and foci of the ellipse with equation 5x2 + 9y2 = 45 are (0, 0), (±3, 0) and (±2, 0).