# Thread: find equation of circle

1. ## find equation of circle

If AB is the diameter of a circle and P another point on the circumference then Euclidean Geometry tells us that angle APB=90 degrees. Use this fact to show that the equation of the circle whose diameter has endpoints
A(x1,x2) and B(x2,y2) is (x-x1)(x-x2)+(y-y1)(y-y2)=0

(all the numbers above should be sub script, sorry)

Any help greatly appreciated.

2. Originally Posted by slaypullingcat
If AB is the diameter of a circle and P another point on the circumference then Euclidean Geometry tells us that angle APB=90 degrees. Use this fact to show that the equation of the circle whose diameter has endpoints
A(x1,x2) and B(x2,y2) is (x-x1)(x-x2)+(y-y1)(y-y2)=0

(all the numbers above should be sub script, sorry)

Any help greatly appreciated.
If P is the point on the circle, then find the slope of the line AP and BP.
Since angle APB 90 degrees the product of the slopes should be -1.