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)
-----------
Pick 2 of the 3 lines between the 3 points and find the perpendicular bisectors of them.
--------
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.
-->
--------------
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:
^2\ +\ (y_1\ -\ k)^2)
where )
is any of the initially given points.
Using the coordinates of the center and the radius, write the standard form equation:
^\ +\ (y\ -\ k)^2\ =\ r^2)
John
My calculator said it, I believe it, that settles it
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