Question

A circular pond is modeled by the equipment x^2+y^2=225. A bridge over the pond is modeled by a segment of the equation x-7y=-75. What are the coordinates of the points where the bridge meets the edge of the pond?

Answer 1

x² + y² = 225
x - 7y = -75

x = 7y - 75

x² + y² = 225
(7y-75)² + y² = 225
(7y - 75)(7y - 75) + y² = 225
49y² - 525y - 525y + 5625 + y² = 225
50y² - 1050y + 5400 = 0
50(y² - 21y + 108) = 0

y² - 21y + 108 ⇒ (y - 12)(y - 9)

x = 7(12) - 75
x = 84 - 75
x = 9 ⇒ (9,12)

x = 7(9) - 75
x = 63 - 75
x = -12 ⇒ (-12,9)