Answer:
(x − 1)² + (y + 19/8)² = 2665/64
Explanation:
General equation of a circle is:
(x − h)² + (y − k)² = r²
If we plug in the three points:
(-5 − h)² + (0 − k)² = r²
(0 − h)² + (4 − k)² = r²
(2 − h)² + (4 − k)² = r²
Simplifying:
(-5 − h)² + k² = r²
h² + (4 − k)² = r²
(2 − h)² + (4 − k)² = r²
If we subtract the second equation from the third:
(2 − h)² − h² = 0
4 − 4h + h² − h² = 0
4 − 4h = 0
h = 1
Plugging into the first two equations:
(-5 − 1)² + k² = r²
1² + (4 − k)² = r²
Simplifying:
36 + k² = r²
1 + (4 − k)² = r²
Subtracting the two equations:
1 + (4 − k)² − (36 + k²) = 0
1 + 16 − 8k + k² − 36 − k² = 0
-8k − 19 = 0
k = -19/8
Plugging into the first equation to find r²:
(-5 − 1)² + (-19/8)² = r²
36 + 361/64 = r²
2665/64 = r²
Therefore, the general equation is:
(x − 1)² + (y + 19/8)² = 2665/64
Graph:
desmos.com/calculator/6jeelftov8