Question

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

$y^2-8x^2-2x-y=0$

Short answer

The graph is of hyperbola.

Step-by-step solution

Step 1. Given information

The equation is$y^2-8x^2-2x-y=0$.

Step 2. Identify the graph.

Consider the equation $y^2-8x^2-2x-y=0$.

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

$\begin{array}{rcl}A& =& -8\\ C& =& 1\\ AC& =& -8\\ & <& 0\end{array}$

So, the equation represents a hyperbola.