Math - Ellipse Problem (Conic Section)

Question

Madison and Crysh are visiting a whispering gallery. Each of them is standing at a focus and is 1 m. from the nearest wall. If the ceiling of the gallery at the center is 4m. high from the floor, how long is the gallery from left to right? What is the distance between Madison and Crysh?

Answer 1

c + 1 = a; b = 4; a² = b² + c²;

a² = 16 + (a - 1)²; a² = 16 + (a - 1)²; 0 = 16 - 2a + 1; 2a = 17; a = 8.5

Equation of ellipse: x²/72.25 + y²/16 = 1.

Length of gallery:L = 2a = 17 m

Distance between people S 2c = 15 m