Question

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

$4x^2-3y^2-8x+6y+1=0$

Short answer

The graph is of hyperbola.

Step-by-step solution

Step 1. Given information

The equation is$4x^2-3y^2-8x+6y+1=0$.

Step 2. Identify the graph.

Consider the equation $4x^2-3y^2-8x+6y+1=0$.

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

$\begin{array}{rcl}A& =& 4\\ C& =& -3\\ AC& =& 4(-3)\\ & =& -12\\ & <& 0\end{array}$

As$AC<0$, the equation represents hyperbola.