Posted by Rachel on Sunday, May 27, 2012 at 9:08pm.
x ^ 2 + y ^ 2 - 6 x - 8 y + 25 = 36
Equation of a circle in standard form :
( x - h ) ^ 2 + ( y - k ) ^ 2 = r ^ 2
x ^ 2 + y ^ 2 - 6 x - 8 y + 25 = 36
x ^ 2 - 6 x + y ^ 2 - 8 y + 25 = 36
( x ^ 2 - 6 x ) + ( y ^ 2 - 8 y ) + 25 = 36
The process involves completing the square separately for the x and y variables.
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( x - 3 ) ^ 2 = x ^ 2 - 2 * x * 3 + 3 ^ 2
( x - 3 ) ^ 2 = x ^ 2 - 6 x + 9 Subtract 9 to both sides
( x - 3 ) ^ 2 - 9 = x ^ 2 - 6 x + 9 - 9
( x - 3 ) ^ 2 - 9 = x ^ 2 - 6 x
x ^ 2 - 6 x = ( x - 3 ) ^ 2 - 9
( y - 4 ) ^ 2 = y ^ 2 - 2 * y * 4 + 4 ^ 2
( y - 4 ) ^ 2 = y ^ 2 - 8 y + 16 Subtract 16 to both sides
( y - 4 ) ^ 2 - 16 = y ^ 2 - 8 y + 16 -16
( y - 4 ) ^ 2 - 16 = y ^ 2 - 8 y
y ^ 2 - 8 y = ( y - 4 ) ^ 2 - 16
__________________________
( x ^ 2 - 6 x ) + ( y ^ 2 - 8 y ) + 25 = 36
( x - 3 ) ^ 2 - 9 + ( y - 4 ) ^ 2 - 16 + 25 = 36
(x - 3 ) ^ 2 + ( y - 4 ) ^ 2 - 25 + 25 = 36
( x - 3 ) ^ 2 + ( y - 4 ) ^ 2 = 36
( x - 3 ) ^ 2 + ( y - 4 ) ^ 2 = 6 ^ 2
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