Question 315531
y^2+2y=x^2+x
is this equation a parabola, circle, ellipse, or hyperbola? how do you know?
It is a hypobola because the x^2 and y^2  have opposite signs when 
arranged on the same side of the equation.
=================================================
Rearrange:
x^2 + x - (y^2+2y) = 0
Complete the square:
(x^2 + x + (1/2)^2) - (y^2+2y+1) = (1/2)^2 - 1
(x+1/2)^2 - (y+1)^2 = -3/4
----
(y+1)^2 - (x+(1/2))^2 = (3/4)
===============================
Cheers,
Stan H.
===============================