Question

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

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

Short answer

The graph is of a circle.

Step-by-step solution

Step 1. Given information

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

Step 2. Identify the graph.

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

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

$\begin{array}{rcl}A& =& 2\\ C& =& 2\\ AC& =& 2\left(2\right)\\ & =& 4\\ & >& 0\end{array}$

So, the equation represents a circle.