1. The problem is to find the equation of a circle given its center and a point on its circumference. 2. The general equation of a circle with center $(h,k)$ and radius $r$ is: $$ (x - h)^2 + (y - k)^2 = r^2 $$ 3. Here, the center is given as $(4,3)$. 4. A point on the circumference is $(-1,1)$. 5. To find the radius $r$, calculate the distance between the center and the point on the circle using the distance formula: $$ r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$ 6. Substitute the values: $$ r = \sqrt{(-1 - 4)^2 + (1 - 3)^2} = \sqrt{(-5)^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29} $$ 7. Now, substitute $h=4$, $k=3$, and $r^2=29$ into the circle equation: $$ (x - 4)^2 + (y - 3)^2 = 29 $$ 8. This is the equation of the circle. Final answer: $$ (x - 4)^2 + (y - 3)^2 = 29 $$