How do use the discriminant test to determine whether the graph $4 x^{2} + 4 x y + y^{2} + 7 x + 8 y = 0$ $4x^2+4xy+y^2+7x+8y=0$ 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

$A x^{2} + B x y + C y^{2} + D x + E y + F = 0$ $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$

And the discriminant is

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

Here,

The equation is

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

The discriminant is

$4^{2} - 4 \times 4 \times 1 = 16 - 16 = 0$ $4^2-4xx4xx1=16-16=0$

This corresponds to a PARABOLA.

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

How do use the discriminant test to determine whether the graph 4x2+4xy+y2+7x+8y=04x^2+4xy+y^2+7x+8y=0 whether the graph is parabola, ellipse, or hyperbola?