Question 3.7.6: Find the equation of the circle that is determined by the po...

Substitution of the xy-coordinates of each of the three points P, Q, and R into (9) gives the three equations

x² + y² + Ax + By + C = 0                           (9)

– A + 5B + C = – 26
5A –  3B + C = – 34
6A + 4B + C = –  52.

Reduction of the corresponding augmented coefficient matrix to reduced row-echelon form (Fig. 3.7.8) yields A = –  4, B = – 2, and C = –  20. Thus the equation of the desired circle is

x² + y² –  4x –  2y –  20 = 0.

To find its center and radius, we complete the squares in x and y and get

(x –  2)² + (y –  1)² = 25.

Thus the circle has center (2, 1) and radius 5 (Fig. 3.7.9).