Answer: The equation of a circle with center (a,b) and radius r is given by:
(x - a)^2 + (y - b)^2 = r^2
In this case, the center is (9,10) and the point on the circle is (7,4). To find the radius, we can use the distance formula between the center and the point on the circle:
r = sqrt((7 - 9)^2 + (4 - 10)^2) = sqrt((-2)^2 + (-6)^2) = sqrt(40)
So, the equation of the circle is:
(x - 9)^2 + (y - 10)^2 = 40
Alternatively, we can also expand the equation to get:
x^2 - 18x + 81 + y^2 - 20y + 100 = 40
Simplifying and rearranging, we get:
x^2 + y^2 - 18x - 20y + 41 = 0
Therefore, the equation of the circle is either (x - 9)^2 + (y - 10)^2 = 40 or x^2 + y^2 - 18x - 20y + 41 = 0.
Explanation: