Find the area of the smallest circle passing through the points (2,4) and (5,1). Express your answer in terms of $\pi$. Answer ... units^2

1. Find the length of the line segment joining the two points

Distance between $(2,4)$ and $(5,1)$:
$d=\sqrt{(5-2)^2+(1-4)^2}$
$=\sqrt{3^2+(-3)^2}=\sqrt{18}=3\sqrt{2}$

2. Use the distance as the diameter of the smallest circle and calculate the area

For the smallest circle passing through the two points, the segment joining them is the diameter.

So
$r=\frac{3\sqrt{2}}{2}$
Area:
$\pi r^2=\pi\left(\frac{3\sqrt{2}}{2}\right)^2$
$=\pi\cdot\frac{18}{4}=\frac{9\pi}{2}$