Question

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

$2x^2+y^2-8x+4y+2=0$

Short answer

An equation represents a graph of an ellipse.

Step-by-step solution

Step 1. Given information

An equation is$2x^2+y^2-8x+4y+2=0$.

Step 2. Identify the graph.

The conic is given by the equation given below.

$2x^2+y^2-8x+4y+2=0$

The conic can be determined calculating the value of $B^2-4AC$.

$\begin{array}{rcl}{B}^2-4AC& =& (0{)}^2-4(2\left)\right(1)\\ & =& -8\end{array}$

The value of $B^2-4AC$is negative and therefore the given conic is an ellipse since $A$is not equal to$B$.