Show that the equation represents a circle by rewriting it in standard form, and find the center and radius of the circle.

x^2+y^2-1/2x+1/2y=-1/16

x^2+y^2+1/2x+2y+1/16=0

x^{2} + y^{2} + 6x + y + 9 = 0

x^2+y^2-1/2x+1/2y=-1/16x^2-2.1/4x + 1/16 + y^2+2.1/4y + 1/16 - 1/16 - 1/16 =-1/16(x-1/4)^2 + (y+1/4)^2 = 1/16this is the standard formcomparing the above equation with standard equation , (x-h)^{2} + (y-k)^{2} = r^{2}we get, h = 1/4 and k = -1/4 and r =1/4so, center is (1/4,-1/4) with radius = 1/4x^2+y^2+1/2x+2y+1/16=0x^2+2.1/4x + 1/16 + y^2+2.1.x + 1 -1/16-1+1/16 =0(x+1/4)^2 +(y+1)^2 = 1this is the standard formcomparing the above equation with standard equation , (x-h)^{2} + (y-k)^{2} = r^{2}we get, h = -1/4 and k = -1 and r =1so, center is (-1/4,-1) with radius = 1

x^{2} + y^{2} + 6x + y + 9 = 0x^{2} + 2.3.x + 9 + y^{2} + 2.1/2y +1/4 - 9 - 1/4 + 9 = 0(x+3)^{2} + (y+1/4)^{2} = 1/4This is the standard form.comparing the above equation with standard equation , (x-h)^{2} + (y-k)^{2} = r^{2}we get, h = -3 and k = -1/4 and r =1/2so, center is (-3,-1/4) with radius = 1/2

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