Please help, I'm confused.
--
Write the general equation for the circle that passes through the points (-5,0), (0,4), and (2,4).

(x − 1)² + (y + 19/8)² = 2665/64

Step-by-step 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

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction