Answer:
x² + y² − 8x − 6y = 0
Step-by-step explanation:
The conic form of a circle is:
x² + y² + Dx + Ey + F = 0
Plugging in the three points:
(1)² + (7)² + D(1) + E(7) + F = 0
(8)² + (6)² + D(8) + E(6) + F = 0
(7)² + (-1)² + D(7) + E(-1) + F = 0
Simplifying:
50 + D + 7E + F = 0
100 + 8D + 6E + F = 0
50 + 7D − E + F = 0
Subtracting the first equation from the third:
(50 + 7D − E + F) − (50 + D + 7E + F) = 0
6D − 8E = 0
3D = 4E
Now if we subtract the third equation from the second:
(100 + 8D + 6E + F) − (50 + 7D − E + F) = 0
50 + D + 7E = 0
150 + 3D + 21E = 0
Substituting:
150 + 4E + 21E = 0
150 + 25E = 0
E = -6
Therefore, D = -8.
Plugging into any equation to find F:
50 + (-8) + 7(-6) + F = 0
F = 0
The equation of the circle is:
x² + y² − 8x − 6y = 0
Graph:
desmos.com/calculator/davg3d3lic
