Find the equation of the circle which is symmetric to the circle (x-2)^2+(y+2)^2=8 with respect to the line y=-x

Question

Find the equation of the circle which is symmetric to the circle (x-2)²+(y+2)²=8 with respect to the line y=-x

please explain

Answer 1

(x - h)² + (y - k)² = r

So, our center, (h,k) is (2,-2), which falls on the graph of y = -x. After all, -2 = -(2), right?

Thus, the circle is symmetric to itself with respect to the line y = -x, so the equation is the same.