SOLUTION: Find an equation of the circle that passes through the points (2,3), (4,5), and (0,-3).

Algebra.Com
Question 1076714: Find an equation of the circle that passes through the points (2,3), (4,5), and (0,-3).
Found 2 solutions by MathLover1, Alan3354:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
Find an equation of the circle that passes through the points (,), (,), and (,).
The standard form equation of a circle is where
and are the and coordinates of the center of the circle
first find coordinates of the center (,) using given points
The first step is to set up these 3 equations by plugging the x- and y-coordinates of the points
(,), (,), and (,) into the circle formula:
.................eq1
..................eq2
.................eq3
----------------------------------------------
.................eq1
..................eq2
...............eq3
--------------------------------------------

.................eq1
..................eq2...............subtract eq2 from eq1
---------------------------------------------------------


............simplify
.............eq1a

h^2 - 4h + k^2 - 6 k + 13 = r^2.................eq1
h^2 + k^2 + 6k + 9 = r^2...............eq3...........subtract eq3 from eq1
------------------------------------------


............divide by -4
..............................eq2a
use
...............eq1a
..............................eq2a
-------------------------------------------------------------subtract eq1a from eq2a





now find
...............eq1a




so, center is at (,)
use one point, h and k to find r
.................eq1




and, your equation is:

(2,3), (4,5), and (0,-3).
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Find an equation of the circle that passes through the points (2,3), (4,5), and (0,-3).
-----------
Use determinants.
For this circle:

|(x^2+y^2)   x   y   1|
|   13       2   3   1|
|   41       4   5   1| = 0
|    9       0  -3   1|

=================
You can make an Excel sheet to solve it.
===================================================================
Or, a geometrical approach:
Find an equation of the circle that passes through the points A(2,3), B(4,5), and C(0,-3).
I labeled the points.
Find the perpendicular bisectors of AB and BC.
The intersection of the bisectors is the center of the circle, (h,k).
The distance from the center to any of the 3 points is the radius, r.
RELATED QUESTIONS

find the equation of the circle that passes through the 3 points (5, -7), (2, -4), and... (answered by solver91311,MathLover1,greenestamps)
the circle passes through the points (0, 0), (O, 5), (3, 3). Find the equation of the... (answered by lwsshak3)
Hi, these are five questions which I need help in Write the general equation for the... (answered by Alan3354,Boreal,solver91311,ikleyn)
Find an equation of the circle that has center (4,-6) and passes through (-3,-4) (answered by josgarithmetic,MathLover1)
Find the equation of the circle that passes through (-2, 1), (4, -3), and... (answered by Alan3354)
Find the equation of the circle that passes... (answered by Alan3354)
Find the equation of the circle which passes through the points (-3,-4),(2,1), and... (answered by Fombitz,Alan3354)
Find an equation of the line that passes through the points (-1, -2) and (4,... (answered by MathLover1)
Find an equation of the line that passes through the points (1,6) and... (answered by solver91311)