# How do use the discriminant test to determine whether the graph 4x^2+4xy+y^2+7x+8y=0 whether the graph is parabola, ellipse, or hyperbola?

Nov 27, 2017

The graph is a parabola.

#### Explanation:

The general equation of a conic is

$A {x}^{2} + B x y + C {y}^{2} + D x + E y + F = 0$

And the discriminant is

${B}^{2} - 4 A C$

Here,

The equation is

$4 {x}^{2} + 4 x y + 1 {y}^{2} + 7 x + 8 y + 0 = 0$

The discriminant is

${4}^{2} - 4 \times 4 \times 1 = 16 - 16 = 0$

This corresponds to a PARABOLA.

graph{4x^2+4xy+1y^2+7x+8y=0 [-10, 10, -5, 5]}