What conic is this equation: x^2+y^2+x-y = 3?

Question

sketch its graph and denote the important information regarding the conic.

Answer 1

x^2 + y^2 + x - y
x^2 + x + y^2 - y = 3

(x^2 + x) + (y^2 - y) = 3
(x^2 + x + (1/4) - (1/4)) + (y^2 - y - (1/4) + (1/4)) = 3
((x^2 + (1/2))^2 - (1/4) + ((y^2 + (1/2))^2 + (1/4)) = 3
(x^2 + (1/2))^2 - (1/4) + (y^2 + (1/2))^2 + (1/4) = 3
(x^2 + (1/2))^2 + (y^2 + (1/2))^2 = 3

Center ((-1/2),(-1/2))
Radius : sqrt(3)

This is a circle, for a graph, go to www.quickmath.com and type in (x^2 + (1/2))^2 + (y^2 + (1/2))^2 = 3

Answer 2

group the x's and group the y's: (x^2+x)+(y^2-y) = 3
complete the square for the x and the y group:
(x+(1/2))^2+(y-(1/2))^2 = 3+(1/4)+(1/4)
(x+(1/2))^2+(y-(1/2))^2 = 3.5
It is a circle with center ((-1/2),(1/2)) and radius sqrt(3.5)

Answer 3

It's a circle, since the quadratic terms are equal and both positive. The other terms relocate the center so that it is not at (0, 0).

Answer 4

I have know idea, and I don't like math!