SOLUTION: How do I write the standard equation for the circle that passes through the points: (-1, 2) (4, 2) (- 3, 4)

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Question 583783: How do I write the standard equation for the circle that passes through the points:
(-1, 2)
(4, 2)
(- 3, 4)
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
How do I write the standard equation for the circle that passes through the points:
(-1, 2)
(4, 2)
(- 3, 4)
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Pick 2 of the 3 lines between the 3 points and find the perpendicular bisectors of them.
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The intersection of the perpendicular bisectors is the center of the circle, (h,k).
The radius is the distance from the center to any of the 3 points, = r.
-->
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Or use determinants.

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Use the idea that the perpendicular bisector of any chord of a circle passes through the center of the circle. Since the given points are on the circle, any pair of the three points are the endpoints of a line segment that is a chord of the circle.

Select 2 of the three given points.

Step 1: Calculate the midpoint of the segment connecting those two points using the midpoint formulas:

and

Step 2: Calculate the slope of the line containing the two selected points using the slope formula:

Step 3: Determine the slope of the perpendicular to the segment. Take the negative reciprocal of the slope calculated in step 2.

Step 4: Derive an equation of the perpendicular bisector of the selected segment by using the point-slope form of an equation, the slope from step 3, and the midpoint from step 1.

Choose a different pair of points and repeat the process.

Take the two equations of the perpendicular bisectors as a 2X2 system and solve for the point of intersection, which is the center of the circle.

Use a modified form of the distance formula to calculate the radius squared:

where is any of the initially given points.

Using the coordinates of the center and the radius, write the standard form equation:

John

My calculator said it, I believe it, that settles it