The general equation of a conic $\displaystyle Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ can tell you the kind of conic it defines even when $\displaystyle B \neq 0$. The following rule applies:

Let $\displaystyle K= B^2-4AC$, then the equation defines

an ellipse if $\displaystyle K < 0$.

a parabola if $\displaystyle K = 0$.

a hyperbola if $\displaystyle K > 0$.

Tell what kind of conic each equation represents. On your

__own graph paper__, graph each function by solving for $\displaystyle y$. (

*Hint*: To do this, you may need the quadratic formula, regarding $\displaystyle y$ as the variable and $\displaystyle x$ as part of the coeffiecient of $\displaystyle y$.

**(a)** $\displaystyle 2x^2 - xy - 10 =0$

**Conic:** hyperbola

**y=** ________________

**(b)** $\displaystyle x^2 + xy +y^2 - 8 = 0$

**Conic:** ellipse

**y=** ________________

**(c)** $\displaystyle x^2 + 2xy + y^2 - 2x = 0$

**Conic:** parabola

**y=** ________________