Answer:
2x² + 5x + 2y² − 12y = 0
Step-by-step explanation:
Equation of a circle is:
(x − h)² + (y − k)² = r²
Given three points, we can write three equations:
(0 − h)² + (0 − k)² = r²
(0 − h)² + (6 − k)² = r²
(2 − h)² + (3 − k)² = r²
Simplifying:
h² + k² = r²
h² + 36 − 12k + k² = r²
4 − 4h + h² + 9 − 6k + k² = r²
Setting the first two equations equal:
h² + k² = h² + 36 − 12k + k²
0 = 36 − 12k
k = 3
Setting the first and third equations equal:
h² + k² = 4 − 4h + h² + 9 − 6k + k²
0 = 4 − 4h + 9 − 6k
4h = 13 − 6k
4h = 13 − 6(3)
4h = -5
h = -5/4
Plugging into the first equation:
h² + k² = r²
(-5/4)² + (3)² = r²
r² = 169/16
r = 13/4
Therefore, the equation of the circle is:
(x + 5/4)² + (y − 3)² = 169/16
Converting to conic form:
x² + 5/2 x + 25/16 + y² − 6y + 9 = 169/16
16x² + 40x + 25 + 16y² − 96y + 144 = 169
16x² + 40x + 16y² − 96y = 0
2x² + 5x + 2y² − 12y = 0
Graph:
desmos.com/calculator/ilzq3xgvbl
