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First we compute the distance between the center and the given point which is exactly the radius
r =
[tex] \sqrt{(x2 - x1) + (y2 - y1)} = \sqrt{9 - 3 + 11 - 7} = \sqrt{10} [/tex]
Now that we know the center and the radius, we can write the equation of a circle with given radius and center:
[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]
where (h,k) represent the coordinates of the center (3,7).
We substitute and obtain
[tex] {(x - 3)}^{2} + {(y - 7)}^{2} = { \sqrt{10} }^{2} \\ {(x - 3)}^{2} + {(y - 7)}^{2} = 10 \\ {x}^{2} - 6x + 9 + {y}^{2} - 14y + 49 = 10 \\ {x}^{2} + {y}^{2} - 6x - 14y + 48 = 0[/tex]