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The equation of the circle that passes through (-1,6) and which has a center at (2,3) can be written as x^2 + y^2 + Ax + By + C = 0. Find A times B times C.

 Apr 27, 2020
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Equation of a circle:  (x - h)2 + (y - k)2  =  r2  where the center is (h, k) and the radius is r.

 

Since the center is (2,3)  h = 2  and  k = 3.

 

To find the radius we need to know the distance from (-1,6) to (2,3).

Using the distance formula:  r  =  sqrt( (2 - -1)2 + (3 - 6)2 )  =  sqrt( (3)2 + (-3)2 )  =  sqrt( 9 + 9 )  =  sqrt( 18 )

Since  r  =  sqrt( 18 )  --->   r2  =  18

 

So, our equation is:  (x - 2)2 + (y - 3)2  =  18

 

Multiplying this out:  (x2 - 4x + 4) + (y2 - 6y + 9)  =  18

 

The equation for the circle is:     x2 + y2 - 4x - 6y - 5  =  0                                                              

 

From here, pick out A, B, and C, and multiply them together.

 Apr 28, 2020

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