Answer
Parabola
Work Step by Step
The discrimination of the equation is found by the expression $B^{2}-4AC$.
It is a parabola if $B^{2}-4AC$ equals 0.
An ellipse if $B^{2}-4AC$ is between 0 and 1.
A hyperbola if $B^{2}-4AC$ is over 1.
The equation in the form
$Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0$
tells us what values to input in the expression. In this problem, the constants $A$, $B$, $C$ are:
$A=2$
$B=-4$
$C=2$
Calculate the discriminant:
$B^{2}-4AC$ = $(-4)^2-4(2)(2)$ = $16-16$ = $0$, which shows that the equation will be a parabola (proven by graph above).
