A circle has the equation $(x-4{)}^2+(y+7{)}^2=10$. Find the center, radius, and intercepts of the circle and then sketch the graph of the circle.

Step 1 ：The equation of a circle is given by $(x-h{)}^2+(y-k{)}^2=r^2$ where $(h,k)$ is the center of the circle and $r$ is the radius. Comparing this with the given equation, we can see that the center of the circle is $(4,-7)$ and the radius is $\sqrt{10}$.

Step 2 ：To find the x-intercepts, we set $y=0$ in the equation and solve for $x$. Similarly, to find the y-intercepts, we set $x=0$ in the equation and solve for $y$.

Step 3 ：The x-intercepts and y-intercepts are complex numbers, which means the circle does not intersect the x-axis or y-axis.

Step 4 ：Final Answer: The center of the circle is at point $(4,-7)$, the radius is $\sqrt{10}$, and there are no real x-intercepts or y-intercepts. The circle does not intersect the x-axis or y-axis. The graph of the circle would be a circle centered at point $(4,-7)$ with a radius of $\sqrt{10}$, and it would not intersect the x-axis or y-axis.

Step 5 ：$$\boxed{{\displaystyle \begin{array}{rl}\text{Center}& :(4,-7)\\ \text{Radius}& :\sqrt{10}\\ \text{X-intercepts}& :\text{None}\\ \text{Y-intercepts}& :\text{None}\end{array}}}$$