A circle in the xy-plane has its center at (3, -2) and passes through the point (7, 1). Which of the following is an equation of the circle?
Correct: A
The standard equation of a circle with center (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2.
Given the center (h, k) = (3, -2), the equation starts as (x - 3)^2 + (y - (-2))^2 = r^2, which simplifies to (x - 3)^2 + (y + 2)^2 = r^2.
To find r^2, we use the fact that the circle passes through the point (7, 1). We can substitute these coordinates into the equation:
(7 - 3)^2 + (1 + 2)^2 = r^2
(4)^2 + (3)^2 = r^2
16 + 9 = r^2
25 = r^2
So, the equation of the circle is (x - 3)^2 + (y + 2)^2 = 25.