Question #N345

In the xy-plane, a circle with center (2, -3) passes through the point (5, 0). What is the radius of the circle?
A. 2
B. 3
C. $\sqrt{10}$
D. $\sqrt{34}$

Correct Answer is: D

The radius of the circle is the distance between the center of the circle and any point on the circle. We can use the distance formula to find the distance between (2, -3) and (5, 0). The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. Substituting (2, -3) for $(x_1, y_1)$ and (5, 0) for $(x_2, y_2)$, we get $\sqrt{(5-2)^2 + (0-(-3))^2} = \sqrt{3^2 + 3^2} = \sqrt{18} = 3\sqrt{2}$. Thus, the radius of the circle is $\sqrt{34}$.