Respuesta :
Answer:
the equation of circle: x² + y² - 4x - 6y - 12 =0
Step-by-step explanation:
To find the equation of the circle that passes through the points (6, 6), (5, 7) and (2, -2), we can substitute the x and y values of the given points into a standard form of equation of circle:
[tex]\boxed{x^2+y^2+Ax+By+C=0}[/tex]
(1) substitute the x and y with (6, 6):
[tex]x^2+y^2+Ax+By+C=0[/tex]
[tex]6^2+6^2+A(6)+B(6)+C=0[/tex]
[tex]6A+6B+C=-72\ ...\ [1][/tex]
(2) substitute the x and y with (5, 7):
[tex]x^2+y^2+Ax+By+C=0[/tex]
[tex]5^2+7^2+A(5)+B(7)+C=0[/tex]
[tex]5A+7B+C=-74\ ...\ [2][/tex]
(3) substitute the x and y with (2, -2):
[tex]x^2+y^2+Ax+By+C=0[/tex]
[tex]2^2+(-2)^2+A(2)+B(-2)+C=0[/tex]
[tex]2A-2B+C=-8\ ...\ [3][/tex]
Combining [1] & [2]
6A + 6B + C = -72
5A + 7B + C = -74
--------------------------- (-)
A - B = 2 ... [4]
Combining [1] & [3]
6A + 6B + C = -72
2A - 2B + C = -8
--------------------------- (-)
4A + 8B = -64
A + 2B = -16 ... [5]
Combining [4] & [5]
A - B = 2
A + 2B = -16
------------------- (-)
-3B = 18
B = -6
Substitute B = -6 into [4]
A - B = 2
A - (-6) = 2
A = -4
Substitute A & B value into [3]
2A - 2B + C = -8
2(-4) - 2(-6) + C = -8
-8 + 12 + C = -8
C = -12
Therefore, the equation of circle: x² + y² - 4x - 6y - 12 =0
