Show that the equation represents a circle by rewriting it in standard form, and

Algebra
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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

x2 + y2 + 6x + y + 9 = 0

Feb 1st, 2015

x^2+y^2-1/2x+1/2y=-1/16
x^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 = 1/16
this is the standard form


comparing the above equation with standard equation , (x-h)2 + (y-k)2 = r2
we get, h = 1/4 and k = -1/4 and r =1/4

so, center is (1/4,-1/4) with radius = 1/4



x^2+y^2+1/2x+2y+1/16=0
x^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 = 1
this is the standard form

comparing the above equation with standard equation , (x-h)2 + (y-k)2 = r2
we get, h = -1/4 and k = -1 and r =1

so, center is (-1/4,-1) with radius = 1


x2 + y2 + 6x + y + 9 = 0
x2 + 2.3.x + 9 + y2 + 2.1/2y +1/4 - 9 - 1/4 +  9 = 0
(x+3)2 + (y+1/4)2 = 1/4
This is the standard form.

comparing the above equation with standard equation , (x-h)2 + (y-k)2 = r2
we get, h = -3 and k = -1/4 and r =1/2

so, center is (-3,-1/4) with radius = 1/2


Feb 1st, 2015

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Feb 1st, 2015
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