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Suppose a classmate missed the lessons on completing the square to find the center and radius of a circle.

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Suppose a classmate missed the lessons on completing the square to find the center and radius of a circle. Explain the process to them. If it helps, use a problem you’ve already done as an example.

Apr 14, 2020

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x^2   + 4x          +  y^2 - 6y    -12    = 0

Standard form of a circle  with center (h,k)   is    (x-h)^2  + (y-k)^2  = r^2

we want to get the red equation into that form to find the center , (h,k)

x^2 + 4x            + y^2 - 6y        - 12     = 0       'complete the square ' for 'x'   by taking 1/2 of the coefficient of  x

then square it and add it to both sides of the equation to keep

everything balanced....

x^2 + 4x  + 4      + y^2 - 6y     - 12      = 4           do the same thing for the 'y' of the equation

x^2 + 4x +4        + y^2 -6y +9    -12   = 4 + 9     Now reduce the   x    and y portions to squares of binomials

(x+2)^2              + (y-3)^2         -12    =  4 + 9        add 12 to both sides

(x+2)2            +  (y-3)2        = 25

(x+2)2   + (y-3)2   =  52              Now you can readily see   h,k     as   (-2,3)    and the radius  = 5

Apr 14, 2020
edited by ElectricPavlov  Apr 14, 2020