Final answer:
The equation of a circle centered at (6, 4) passing through (2, 1) is obtained by calculating the radius using the distance formula, resulting in a radius of 5. Hence, the equation is (x - 6)^2 + (y - 4)^2 = 25.
Step-by-step explanation:
The equation of a circle with center (6, 4) that passes through the coordinate (2, 1) can be determined by first calculating the radius of the circle, which is the distance between the center and a point on the circle. We use the distance formula to determine the radius:
Distance = √((x_2 - x_1)^2 + (y_2 - y_1)^2)
Substituting the given points, we have:
Radius = √((2 - 6)^2 + (1 - 4)^2) = √((-4)^2 + (-3)^2) = √(16 + 9) = √25 = 5
Now we have the radius, so we can write the equation of the circle:
(x - 6)^2 + (y - 4)^2 = 5^2
Therefore, the correct equation of the circle is:
(x - 6)^2 + (y - 4)^2 = 25