College Algebra, Chapter 2, 2.2, Section 2.2, Problem 62

Find an equation of the circle lies in the first quadrant, tangent to both $x$ and $y$ axis and with radius 5.

If the circle lies in the first quadrant, then its center is positive. And if the circle is tangent to both axes and with radius 5, then it pass through the intercepts of $x (5, 0)$ and $y (0,5)$. Thus, its center is 5 units from $x$ and $y$ axes which is $(5,5)$. Recall that the general equation for the circle with circle $(h,k)$ and radius $r$ is..


$\begin{equation} \begin{aligned} (x - h)^2 + (y - k)^2 =& r^2 && \text{Model} \\ \\ (x - 5)^2 + (y - 5)^2 =& 5^2 && \text{Substitute the given} \\ \\ (x - 5)^2 + (y - 5)^2 =& 25 && \end{aligned} \end{equation}$