Math
posted by Rachel on .
write the equation of the circle in standard form. find the center, radius, intercepts, and graph the circle. x^2+y^26x8y+25=36

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.
____________________________________
( 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