Write the equation of the following circles in standard form: (x - h)^2 + (y - k)^2 = r^2.
1. x^2 + 14x + y^2 - 12y = 10
2. x^2 - 4x + y^2 - 6y = 15
+23245 1) You need to complete the square for both the x-component and the y-component.
(x2 + 14x ) + (y2 - 12y ) = 10
To complete the square for the x-component, divide the coefficient of the x-term by 2 and square this answer, then add
this number to both sides: 14 / 2 = 7 ---> 72 = 49
(x2 + 14x + 49) + y2 - 12y = 10 + 49
To complete the square for the y-component, divide the coefficient of the y-term by 2 and square this answer, then add
this number to both sides: -12 / 2 = -6 ---> (-6)2 = 36
(x2 + 14x + 49) + (y2 - 12y + 36) = 10 + 49 + 36
Now factor:
(x + 7)2 + (y - 6)2 = 95
