Question 636257
Write the equation of the circle in standard form.  Find the center, radius, intercepts, and graph the
circle.
x^2+y^2+8x+2y+8=0
**
Standard form of equation for a circle: {{{(x-h)^2+(y-k)^2=r^2}}}, (h,k)=(x,y) coordinates of center, r=radius.
x^2+y^2+8x+2y+8=0
complete the square
x^2+8x+y^2+2y+8=0
(x^2+8x+16)+(y^2+2y+1)=-8+16+1
Equation:
{{{(x+4)^2+(y+1)^2=9}}}
..
r^2=9
radius=3
..
center:(-4,-1)
..
x-intercepts:
set y=0
(x+4)^2+1=9
(x+4)^2=8
x+4=±√8
x=-4±√8
x≈-6.83
or
x≈-1.17
..
See graph below:
y=±(9-(x+4)^2)^.5-1

{{{ graph( 300, 300, -10, 10, -10, 10, (9-(x+4)^2)^.5-1,-(9-(x+4)^2)^.5-1) }}}