<PRE><B>Question 190691</B>
determine whether the following equations represent a parabola, circle, ellipse or hyperbola 
4x^2 + 6y^2 - 4x - 9y + 12 = 0
A theoretical ellipse.  It has x^2 and y^2 terms added with differing coefficients.  However, the axes are less than zero. If the last term is -12, then it&#39;s an ellipse.
--------------------------
3x^2 + 2x - 5y + 12 = 0 
A parabola.  Only x is 2nd degree.
------------------
4x^2 + 4y^2 -4x + 9y + 1 = 0 
A circle.  x^2 and y^2 with coefficient 4.
-------------------
9x^2 + 12 y^2 + 4x + 4y + 4 = 0 
A theoretical ellipse.  It has x^2 and y^2 terms added with differing coefficients.  However, the axes are less than zero. If the last term is -4, then it&#39;s an ellipse.
-----------------------------------
5x^2 - 2y^2 + 2x - 6y - 6 = 0
A hyperbola.  The x^2 and y^2 terms have different signs.
------------------------
How do I determine this?
</PRE>