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.