.
The line x-y-8 = 0 is perpendicular to the line x = -y.
So, we have a right-angled triangle.
Its side y = -1 is horizontal; it represents the hypotenuse.
The endpoints of the hypotenuse are
(1,-1) (intersection of x= -y and y= -1), and
(7,-1) (intersection of x-y-8 = 0 and y= -1).
In the right-angled triangle, the center of the circumscribed circle lies at the midpoint of the hypotenuse.
Hence, in our case the center of the circumscribed circle is the point (4,-1).
The radius of the circle is half-length of the hypotenuse, i.e. 3.
Hence, the equation of the circle is
= 9 or, which is the same,
= 9.
Solved.
