Answer:
IG: yiimbert
The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
We are given that the center of the circle is (2, 3) and it contains the point (7, 15). To find the radius, we can use the distance formula between the center and the given point:
r = sqrt[(7 - 2)^2 + (15 - 3)^2]
r = sqrt[25 + 144]
r = sqrt(169)
r = 13
Substituting the given values into the equation of a circle, we get:
(x - 2)^2 + (y - 3)^2 = 13^2
Expanding the terms, we get:
x^2 - 4x + 4 + y^2 - 6y + 9 = 169
Simplifying and rearranging, we get:
x^2 - 4x + y^2 - 6y = 156
Therefore, the equation of the circle with center (2, 3) containing the point (7, 15) is:
x^2 - 4x + y^2 - 6y = 156