Question

find the equation of the circle shown in the figure.

Explanation:

Step1: Identify the center

The center of the circle is at the mid - point between the x - intercept and y - intercept. The circle touches the x - axis at $x=-6$ and the y - axis at $y = 6$. So the center $(h,k)=(-6,6)$.

Step2: Determine the radius

The radius $r$ is the distance from the center $(-6,6)$ to the x - axis (or y - axis in this case). The distance from the point $(-6,6)$ to the x - axis is 6. So $r = 6$.

Step3: Use the standard circle equation

The standard equation of a circle is $(x - h)^2+(y - k)^2=r^2$. Substitute $h=-6$, $k = 6$ and $r = 6$ into the equation.
$(x+6)^2+(y - 6)^2=36$

Answer:

$(x + 6)^2+(y - 6)^2=36$