(c(t))2+(r(t))2=k, where k is a constant

Question

(c(t))²+(r(t))²=k, where k is a constant

prove that c(t)*c'(t)=-r(t)*r'(t)

Answer 1

Differentiate (c(t))² + (r(t))² = k with respect to t:

2c(t)c'(t) + 2r(t)r'(t) = 0

By algebraic manipulation

c(t)c'(t) = -r(t)r'(t)