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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

 Apr 27, 2020
 #1
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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)  + y- 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)  + (y- 12y + 36)  =  10 + 49 + 36

     

      Now factor:

 

      (x + 7)2 + (y - 6)2  =  95

 Apr 27, 2020

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