A circle passes through the origin (0, 0) and has its center at (3, 4). What is the equation of the circle?
Correct: B
The standard equation of a circle with center (h, k) is (x - h)^2 + (y - k)^2 = r^2.
Given the center (h, k) = (3, 4), the equation starts as (x - 3)^2 + (y - 4)^2 = r^2.
Since the circle passes through the origin (0, 0), we can use these coordinates to find r^2.
Substitute x = 0 and y = 0 into the equation:
(0 - 3)^2 + (0 - 4)^2 = r^2
(-3)^2 + (-4)^2 = r^2
9 + 16 = r^2
25 = r^2
So, the equation of the circle is (x - 3)^2 + (y - 4)^2 = 25.