Related Rates Question (Calculus)?

Question

If x^2 + y^2 = 25 and dy/dt = 6, find dx/dt when y = 4.


(remember, we're looking for dx/dt, not dy/dt)

Answer 1

x² + y² = 25

Solve for x when y = 4

x² = 25 - y² = 25 - 16 = 9
x = ±3

Calculate dy/dx.

2x + 2y(dy/dx) = 0
x + y(dy/dx) = 0
dy/dx = -x/y = ±3/4

dy/dx = (dy/dt) / (dx/dt)
dx/dt = (dy/dt) / (dy/dx) = 6 / (±3/4) = ±24/3 = ±8