this is probably a conic section
complete the squaer for x and y simultaniously
gropu x's and y's
(x²-4x+4)+(y²+2y+1)=4
factor
(x-2)²+(y+1)²=4
(x-2)²+(y+1)²=2²
this is the equation of a circle
for
(x-h)²+(y-k)²=r²
the center is (h,k) and the readius is r
we have
(x-2)²+(y+1)²=2²
(x-2)²+(y-(-1))=2²
center is (2,-1) and the radius is 2
to graph
graph the point (2,-1)
go 2 units up and down and left and right from (2,1) and make a circle or use a string 2 units in legnth (plot points (2,1), (2,-3), (0,-1), (4,-1) and connect to make a circle)
circle with center (2,-1) and radius 2
(x-2)²+(y+1)²=2²
