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?

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Answer 1 · 2017-11-27T06:41:26

The graph is a parabola.

The general equation of a conic is

#Ax^2+Bxy+Cy^2+Dx+Ey+F=0#

And the discriminant is

#B^2-4AC#

Here,

The equation is

#4x^2+4xy+1y^2+7x+8y+0=0#

The discriminant is

#4^2-4xx4xx1=16-16=0#

This corresponds to a PARABOLA.

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