Find Equation of Circle: A(2,2) & B(5,3), y=x+1

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To find the equation of the circle passing through points A(2,2) and B(5,3) with its center on the line y=x+1, the general circle equation (x-p)² + (y-q)² = r² is used. Substituting points A and B into the equation yields a relationship between p and q, resulting in 3p + 2q = 13. Since the center (p,q) lies on the line y=x+1, it can be expressed as q=p+1. By substituting this into the earlier equation, the values of p and q can be determined, leading to the complete equation of the circle.
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how would you find the equation of a circle : (x-p)^2 + (y-q)^2=r^2 with this given info:

the circle passes through A(2,2) and B(5,3) and its centre is on the line defined by y=X+1
 
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Plug the two points in the equation and then you get an equation with p and q which should look like 3p+2q=13.

since the center is on the line y=x+1, and the center of the circle is supposed to be (p,q). So q=p+1.

then solve for the equation.
 

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