Coordinates

 

In terms of pi, what is the area of the circle defined by the equation 2x^2+2y^2+10x-6y-48=x^2+y^2-2x+4y-10     

 

                                              2x² + 2y² + 10x – 6y – 48  =  x² + y² – 2x + 4y – 10     

 

Combine like terms                          x² + y² + 12x – 10y  =  – 10     

 

Rearrange & add parentheses        (x² + 12x    )  +  (y² – 10y    )  =  – 10     

in preparation to complete sqs     

 

Complete the squares. Anything     (x² + 12x + 36)  +  (y² – 10y + 25)  =  – 10 + 36 + 25     

added to the left side, has to be     

added to the right side also.     

 

Simplify                                            (x + 6)²  +  (y – 5)²  =  51     

 

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

where x and y locate the     

center and r is the radius.     

 

So r² of this circle is 51.  Area of a circle is π r².  So the area is 51 π.     

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