Question #N273
In the xy-plane, a circle has a radius of 5 and a center at (3, 2). Which of the following points lies on the circle?
A. (3, 7)
B. (8, 2)
C. (3, -3)
D. (-2, 2)
Correct Answer is: B
The standard form of the equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. Substituting the given values, the equation of the circle is (x - 3)^2 + (y - 2)^2 = 25. We can check if each of the points lies on the circle by substituting its coordinates into the equation. Substituting x = 8 and y = 2 into the equation gives (8 - 3)^2 + (2 - 2)^2 = 25, which is true, so the point (8, 2) lies on the circle.