Find circle passing through two points and center lying on a line

[petuniac]

Homework Statement

Find the equation of a circle that passes through the points A(2,2) and B(5,3) and has its centre on the line y = x +1

Homework Equations

(x-h)^2 + (y-k)^2 = r^2

The Attempt at a Solution

can get 2 equations knowing the 2 points the circle passes through but still have 3 variables and am not sure how to use the equation for the centre

(2-h)^2 + (2-k)^2 = r^2

(5-h)^2 + (3-k)^2 = r^2


How do I solve from here?

 

[konthelion]

What is h in terms of k?

 

[HallsofIvy]

Any perpendicular bisector of a chord is a radius- i.e. passes through the center of the circle.

What is the center point of the interval AB? What is the slope of the line AB? What is the slope of a line perpendicular to that? What is the equation of the perpendicular bisector of AB? Where does that line intersect y= x+1?

 

[petuniac]

thanks!