Circle and rate

Problem:



Solution:

Question 11)
The radius squared can be computed as $(3 - 6)^2 + (-2-5)^2 = 58$.
Therefore the equation of the circle is $(x - 3)^2 + (y + 2)^2 = 58$.

Question 12)
The radius $r$ as a function of $t$ is simply $r(t) = 2 + 1.3t$.
Therefore the area is given by $f(t) = \pi r(t)^2 = \pi (2 + 1.3t)^2$.

Question 13) Require calculus
No, to see that, notice the rate of change of radius is $\frac{df}{dt} = 2(1.3)\pi(2 + 1.3t)$ which is not a constant, therefore the rate of change of area is not constant.