Answer :

ollieboyne
The equation represents a circle.

If you factorise the equation, you get:

[tex]x^2 + y^2 + 2x +1 =0 \\(x+1)^2-1+(y)^2=0\\(x+1)^2+y^2=1[/tex]

This final equation shows the equation of a circle, as a circle's equation is given as:

[tex](x+a)^2+(y+b)^2=r^2[/tex]
olemakpadu
It a circle because, the equation is a degree 2 equation. That is squared.

The coefficient of x^2 and y^2 are the same.

There is no term term xy.

And a parabola is of the form y^2  =  4ax    or  x^2 = 4ay.

And an ellipse is of the form:    (x^2)/(a^2)  +  (y^2)/(b^2)  =  1.