Answer:
8x² + 8y² - 79x - 32y + 95 = 0
D = -79
E = - 32
F = 95
Step-by-step explanation:
Solve this equation as you normally would, but don't forget about the 8's
General equation of a circle: x² + y² + dx + ey + f = 0
First plug in each point one by one
8(1)² + 8(1)² + d(1) + e(1) + f = 0
8 + 8 + d + e + f = 0, or d + e + f = -16
Point (1, 1): d + e + f = -16
Point (1, 3): d + 3e + f = -80
Point (9, 2): 9d + 2e + f = -680
Subtract the second equation from the first
d + e + f = -16
- (d + 3e + f = -80)
This equals -2e = 64
Subtract the third equation from the first, which yields -8d + e = 600
Now use those last two equations to find d, e, and f
To find d:
-2e = 64
- (-8d + e = 600)
→ -2e = 64
8d - e = - 600
Divide the top equation by negative 2
e = -32
8d - e = -600
→ 8d = - 632
d = -79
Use the known value of d to plug into either equation -2e = 64, or -8d + e = 600 to find e, and then do the same for f
Doing so will result in
d = -79
e = - 32
f = 95
Remember to plug in the values of d, e, and f into the original equation and use one of the points to check if it's correct, hope this helped!
