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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= 

 Sep 16, 2019
 #1
avatar+104869 
+2

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

 

 

 

cool cool cool

 Sep 16, 2019

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