Posted by Sally on Thursday, July 2, 2009 at 6:01pm.
Write the standard for of the equation of the circle that passes through the points at (0,8),(8,0),and (16,8). Then identify the center and radius of the circle.

Math  MathMate, Thursday, July 2, 2009 at 6:35pm
By inspection, the centre of the circle is at (8,8), since the three given points form a righttriangle in which the hypothenus is the diameter (0,8),(16,8).
The radius is half the diameter, namely (160)/2=8
The standard form of a circle with centre at (xo,yo) and radius of R is
(x/xo)^{2} + (y/yo)^{2} = R^{2}
Can you take it from here?
Note:
If you are looking for the general case of a circle passing through three distinct points P1(x1,y1), P2(x2,y2) and P3(x3,y3), it can be obtained by evaluating the following 4x4 determinant:
x^{2} + y^{2} x y 1
x1^{2} + y1sup>2 x1 y1 1
x2^{2} + y2sup>2 x2 y2 1
x3^{2} + y3sup>2 x3 y3 1

Math  MathMate, Thursday, July 2, 2009 at 6:37pm
Sorry, the determinant does not show up very well, and there was a typo:
x^{2} + y^{2} x y 1
x1^{2} + y1^{2} x1 y1 1
x2^{2} + y2^{2} x2 y2 1
x3^{2} + y3^{2} x3 y3 1

Math  MathMate, Thursday, July 2, 2009 at 9:42pm
Please ignore the following format testing:
<pre>
x^{2}+ y^{2} x1 y1 1
x1^{2}+y1^{2} x1 y1 1
x2^{2}+y2^{2} x2 y2 1
x3^{2}+y3^{2} x3 y3 1
</pre>
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