Question 1033358

Write the standard form of the equation for the circle that passes through the points (-2, 30), (-19, -1), and (12, -18). Then identify the center and the radius.

A.(x - 6)² + (y - 5)² = 625; center (6, 5); r = 25
B.(x + 5)² + (y + 6)² = 625; center (5, 6); r = 25
C.(x - 5)² + (y - 6)² = 625; center (5, 6); r = 25
D.(x + 6)² + (y + 5)² = 625; center (6, 5); r = 25
<pre>The following sytem of equations, in 3 unkowns (h, k, r), was derived:
{{{matrix(1,2, h^2 + 4h + k^2 - 60k - r^2 = - 904, "-------- eq (i)")}}}
{{{matrix(1,2, h^2 + 38h + k^2 + 2k - r^2 = - 362, "-------- eq (ii)")}}}
{{{matrix(1,2, h^2 - 24h + k^2 + 36k - r^2 = - 468, "------- eq (iii)")}}}

Subtracting eq (ii) from (i) and (iii) from (i) yield the following reduced system, in 2 unknowns:
– 17h – 31k = - 271, and
   7h – 24k = - 109
When solved, we find (h, k), or center to be (5, 6)

Using the center and one of the given coordinate points result in a radius of 25, so CHOICE C is the correct response.