SOLUTION: Find the equation of the circle through the points (5,1),(4,6)(2,-2)

Question 800665: Find the equation of the circle through the points (5,1),(4,6)(2,-2)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Use the fact that the perpendicular bisector of a chord of a circle passes through the center of the circle.

Label your points A, B, and C. Doesn't matter which is which. Draw segments AB and BC

Use the slope formula to find the slope of the line containing segment AB.

where

and

are the coordinates of the given points.

Then do the same thing for the line containing segment BC.

Use the midpoint formulas to calculate the midpoints of segments AB and BC.

and

Use the negative reciprocal of the slope of the line containing segment AB and the coordinates of the midpoint of segment AB in the point-slope form of an equation of a line to derive an equation of the perpendicular bisector of segment AB.

where

are the coordinates of the given point and

is the given/calculated slope.

Repeat to find an equation of the perpendicular bisector of segment BC.

Use any convenient method to solve the 2X2 system comprised of the perpendicular bisector equations you just derived. The point of intersection will be the center of the circle.

Use the distance formula with the center and any one of the three given points to determine the radius of the circle. You can use the modified form of the distance formula shown below because you actually need the radius squared to complete the circle equation.