Answer:
x² + y² - 3x - 13y + 18 = 0
Explanation:
Recall that the general equation of a circle looks something like this:
x² + y² + Ax + By + C = 0
substituting each of the points into the equation we get:
for (-1,2)
(-1)² + (2)² + A(-1) + B(2) + C = 0
1 + 4 -A+2B + C = 0
-A + 2B + C + 5 = 0 ------------ eq 1
for (4,2)
(4)² + (2)² + A(4) + B(2) + C = 0
16 + 4 + 4A + 2B + C = 0
4A + 2B + C + 20 = 0 ------------- eq 2
for (-3,4)
(-3)² + (4)² + A(-3) + B(4) + C = 0
9 + 16 -3A + 4B + C = 0
-3A + 4B + C + 25= 0 ----- eq 3
Now we have a system of equations with 3 equations and 3 unknowns.
Solving for A, B and C, we eventually get:
A = -3, B = -13, C = 18
Substituting these into the general equation:
x² + y² + Ax + By + C = 0
x² + y² - 3x - 13y + 18 = 0