Answer:
Explanation:
Let's first find the coordinates of the center of the circle. Since the circle passes through the point (1, 2), we know that this point is on the circle. Therefore, the distance from the center of the circle to the point (1, 2) is equal to the radius of the circle. We can use the distance formula to find the distance from the center of the circle to the point (1, 2):
sqrt((x - 1)^2 + (y - 2)^2) = 5
Squaring both sides, we get:
(x - 1)^2 + (y - 2)^2 = 25
Expanding the left side, we get:
x^2 - 2x + 1 + y^2 - 4y + 4 = 25
Simplifying, we get:
x^2 - 2x + y^2 - 4y - 20 = 0
Completing the square for the x and y terms, we get:
(x - 1)^2 - 1 + (y - 2)^2 - 4 - 20 = 0
Simplifying, we get:
(x - 1)^2 + (y - 2)^2 = 25
Therefore, the equation of the circle is:
(x - 1)^2 + (y - 2)^2 = 2