related rate calc 1

Question

A jogger runs around a circular track of radius 65 ft. Let (x,y)(x,y) be her coordinates, where the origin is the center of the track. When the jogger's coordinates are (39, 52), her xx-coordinate is changing at a rate of 1818 ft/s. Find dy/dtdy/dt.

Answer 1

Equation of the circular track is x² + y² = 65²

^{Differentiate implicitly with respect to t to get 2x(dx/dt) + 2y(dy/dt) = 0}

Let x = 39, y = 52, and dx/dt = 1818. Then solve for dy/dt.