Question

In Problem, identify the graph of each equation without completing the squares.

$3x^2-2y^2+6x+4=0$

Short answer

The equation represents the graph of hyperbola.

Step-by-step solution

Step 1. Given information

The given equation is$3x^2-2y^2+6x+4=0$.

Step 2. Identify the graph.

Consider the equation $3x^2-2y^2+6x+4=0$

Compare this equation with $A{x}^2+C{y}^2+Dx+Ey+F=0$.

$\begin{array}{rcl}A& =& 3\\ C& =& -2\\ AC& =& 3(-2)\\ & =& -6\\ & <& 0\end{array}$

As$AC<0$, therefore this equation represents hyperbola.