Question

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.

Answer 1

By inspection, the centre of the circle is at (8,8), since the three given points form a right-triangle in which the hypothenus is the diameter (0,8),(16,8).

The radius is half the diameter, namely (16-0)/2=8
The standard form of a circle with centre at (xo,yo) and radius of R is
(x/xo)² + (y/yo)² = R²
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:

x² + y² x y 1
x1² + y1sup>2</sup> x1 y1 1
x2² + y2sup>2</sup> x2 y2 1
x3² + y3sup>2</sup> x3 y3 1

Answer 2

Sorry, the determinant does not show up very well, and there was a typo:

x² + y² x y 1
x1² + y1² x1 y1 1
x2² + y2² x2 y2 1
x3² + y3² x3 y3 1

Answer 3

Please ignore the following format testing:
<pre>
x²+ y² x1 y1 1
x1²+y1² x1 y1 1
x2²+y2² x2 y2 1
x3²+y3² x3 y3 1
</pre>