Question

if the endpoints of a circle's diameter are (6,2) and (0,-6), what is the area of the circle

Answer 1

you might know this as the distance function.

Answer 2

Via the euclidean norm we have that the radius is
$$r = \frac{|a - b|}{2}$$
Or in other words where \(a=(6,2)\) and \(b=(0,−6)\) we have
$$r = \frac{\sqrt{(0 - 6)^2 + (-6 - 2)^2}}{2} = \frac{\sqrt{36 + 64}}{2} = \frac{10}{2} = 5$$
So its just \(5^2\pi\) or \(25\pi\)