Question 1076714
Find an equation of the circle that passes through the points (2,3), (4,5), and (0,-3).
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Use determinants.
For this circle:
<pre>

|(x^2+y^2)   x   y   1|
|   13       2   3   1|
|   41       4   5   1| = 0
|    9       0  -3   1|
</pre>
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You can make an Excel sheet to solve it.
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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.
{{{(x-h)^2 + (y-k)^2 = r^2}}}