Find the equation of the circle whose center is $\left(-7, -3\right)$ and radius is $10$.
Center $= \left(h, k\right) = \left(-7, -3\right)$
Radius $= r = 10$
Equation of circle is $\;$ $\left(x - h\right)^2 + \left(y - k\right)^2 = r^2$
i.e. $\;$ $\left(x + 7\right)^2 + \left(y + 3\right)^2 = 10^2$
i.e. $\;$ $x^2 + 14x + 49 + y^2 + 6y + 9 = 100$
i.e. $\;$ $x^2 + y^2 + 14x + 6y - 42 = 0$