Find the center C xy of the circle passing through points P2

Find the center C= (x,y) of the circle passing through points P=(22,33), Q=(28,13), and R=(44,7.

Solution

Calculating the equation passing through the mid point of P and Q and perpendicular to PQ

Mid Point => ( -3 , 23 )

Slope of PQ => ( 33 - 13 / 22 + 28 ) = 2/5

Slope of Perpendicular to PQ => -5/2

Equation => ( y - 23 ) = -5/2 ( x + 3 )

Calculating the equation passing through the mid point of Q and R and perpendicular to QR

Mid Point => ( 8 , 10 )

Slope of PQ => ( 13 - 7 / -28 - 44 ) = -1/12

Slope of Perpendicular to PQ => 12

Equation => ( y - 10 ) = 12 ( x - 8 )

Intersection point of both equations or Center : ( 7 , -2 )

Distance between Center and P => ( (22-7)² + (33 + 2)² ) = 558

Therefore , the equation of the circle : (x - 7)² + (y + 2)² = ( 558 )²

(x - 7)² + (y + 2)² = 1450