Square rstu is inscribed in circle p. given the coordinates of the vertices of the square, find the equation of circle p.
r(0, 4), s(6, 2), t(4, -4), and u(-2, -2)

(x - 2)2 + y2 = 68
(x + 2)2 + y2 = 20
(x - 2)2 + y2 = 20

The answer

R(0, 4), S(6, 2), T(4, -4), and U(-2, -2) pass through the circle P, so these points must verified one the equations.
let' s take for example
R(0,4)
(0-2)² +4² = 4+16 =20, R passes though (x - 2)2 + y2 = 20
S(6, 2),
(6-2)² +2² = 16+4=20, S passes though (x - 2)2 + y2 = 20
T(4, -4),
(4-2)² + (-4)² = 4+16=20, T passes though (x - 2)2 + y2 = 20
U(-2, -2),
(-2-2)² + (-2)²= 16+4=20, U passes though (x - 2)2 + y2 = 20

so the equation of the circle is (x - 2)2 + y2 = 20