+318 Show that the equation represents a circle by rewriting it in standard form.
x^2+y^2-1/4x+1/4y=1/32
standard form=
Find the center and radius of the circle.
(x,y)=( )
r=
+128475 x^2+y^2- 1/4x + 1/4y=1/32 rewrite as
x^2 - (1/4)x + y^2 + (1/4)y = 1/32 complete the square on x and y
Take 1/2 of 1/4 =1/8 square it = 1/64 add it twice to both sides
[ x^2 - (1/4)x + 1/64] + [ y^2 + (1/4)y + 1/64 ] = 1/32 + 1/64 + 1/64
Factor the terms in both brackets and simplify the right side
( x - 1/8)^2 + ( y + 1/8)^2 = 1/32 + 2/64
(x - 1/8)^2 + (y + 1/8)^2 = 1/32 + 1/32 [ 1/32 + 1/32 = 2/32 = 1/16 ]
(x - 1/8)^2 + ( y + 1/8)^2 = 1/16
The center is (1/8, - 1/8)
The raduis = sqrt (1/16) = 1/4
