Which of the following is the correct definition of a circle found within a plane in terms of a center (h, k) and radius r?

Find the center and radius of the circle given by ${(x-7)}^2+{(y+2)}^2=121$.

Convert $x^2+y^2+\frac{1}{3}x-\frac{5}{2}y-1=0$ into standard form.

Decide whether $x^2+y^2+2x+4y+10=0$ represents a real circle. Explain your reasoning to justify.

Compute ${\left(\frac{b}{2}\right)}^2$ for $b=-7$, a step used when completing the square for $x^2-7x$.