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Topic: Three Points and a Circle
Replies: 3   Last Post: Mar 1, 2012 11:18 AM

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Bret Jolly

Posts: 13
Registered: 12/6/04
Re: Three Points and a Circle
Posted: Aug 2, 1993 11:14 AM
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The question is how to calculate the Cartesian equation
of a circle given the coordinates of three of its points.

Let the points be (x1,y1), (x2,y2), and (x3,y3). Then
the circle is given by

/ \
| 1 x y x^2 + y^2 |
det | 1 x1 y1 x1^2 + y1^2 | = 0
| 1 x2 y2 x2^2 + y2^2 |
| 1 x3 y3 x3^2 + y3^2 |
\ /

This equation is clearly a circle from its form, and
it passes through each of the three points because when
(x,y) equals one of those points, two rows of the determinant
will be the same.

Similar techniques can be used for many other figures.

Regards, Bret
troly@math.ucla.edu





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