Question 1 What is the equation of the ellipse (see picture below)?

-- Answer -- x/25 + y/9 = 1

Center = (0, 0)

Distance from the center to the edge of the conic in the x direction = 5

Distance from the center to the edge of the conic in the x direction = 3

(x - 0) / 5² + (y - 0) / 3² = 1

Question 2 What is the center, height and width of the ellipse, based on the equation (x - 3)² / 64 + (y + 4)² / 81 = 1?

-- Answer -- (3, -4) is the center and the diameters are 16, 18

Center => (3, -4)

Diameters for a => √64 = a, a = 8, 2a = 16

Diameter for b => √81 = a, a = 9, 2a = 18

Question 3 Given the ellipse x² / 9 + (y - 5)² / 15 = 1, if point, (3, y) is on the ellipse, what is y coordinate?

-- Answer -- (4, 5)

Stick (4, y) into the ellipse equation

3² / 9 + (y - 5)² / 15 = 1 => 9 / 9 + (y - 5)² / 15 = 1

(y - 5)² = 0, y = 5