If x2+y2=64 and dx/dt=5, find dy/dt when y is positive and

Question

If x^2+y^2=64 and dx/dt = 5, find dy/dt when y is positive and...

a) x=0

b) x=1

c) x=4

Answer 1

We differentiate by time t: 2xdx/dt + 2ydy/dt = 0; dy/dt = - x/ydx/dt

a) x = 0, y = 8 and dy/dt = - 0/8·5 = 0

b) x = 1, y = √63 and dy/dt = - 1/√63·5 = - 0.63

c)x = 4√, y = √48 and dy/dt = - 4/√48·5 = - 2.89