circle

 

Find the standard equation of the circle defined by the equation x^2 + y^2 +8x - 12y + 43 = 0     

 

As you may have deduced from the answer choices,

you are going to have to complete those squares.     

 

The standard equation of a circle is (x – h)² + (y – k)²  =  r²     

 

 Starting with                                      x² + y² + 8x – 12y + 43  =  0     

 

Rearrange and add parentheses      (x² + 8x     ) + (y² – 12y     ) + 43  =  0     

 

You need to add 16 to the x and 36 to the y.     

To keep the equation in balance you have to     

subtract the same amount that you add.     

 

                                                          (x² + 8x + 16) + (y² – 12y + 36) + 43 – 52  =  0     

 

                                                          (x + 4)² + (y – 6)² – 9  =  0     

 

Normally, you would take that 9 over to the right of the equals sign     

but this is the form in which the choices of answer were presented.     

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