Thread: Find the equation of the circle that passes through three points.

A ( 3, 1) B ( 2,4) C (-1, 2)

some things that go with this equation

-midpoint
-distance
-perpendicular bisector
-M1-M2= -1
-Simultaneous equations

this is what i have so far i don't know if its correct
(3-a)2 + (1-b)2 = r2 those 2's r squared im new to this and i just plugged in for the rest.

Correct me if im wrong please and help me out if you can
thank you.

Originally Posted by Pre-Calc

A ( 3, 1) B ( 2,4) C (-1, 2)

some things that go with this equation

-midpoint
-distance
-perpendicular bisector
-M1-M2= -1
-Simultaneous equations

this is what i have so far i don't know if its correct
(3-a)2 + (1-b)2 = r2 those 2's r squared im new to this and i just plugged in for the rest.

Correct me if im wrong please and help me out if you can
thank you.

you are doing fine...

the standard equation of a circle is



from your equation a is h and b is K, it would probably be better to use the standard equation since that is what is commonly used.

first find the center of the circle by doing a simultaneous equations of the 2 perpendicular bisectors
of the lines AB and BC
then you have the center C(h,k)

to find the perpendicular bisector of line AB


squaring both sides yields

next expand




continue with BC then find H,K by simultanuous equation

Thank you I understand it now.