How do use the discriminant test to determine whether the graph $x^2+2xy-3y^2+5x+6y-100=0$ whether the graph is parabola, ellipse, or hyperbola?

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How do use the discriminant test to determine whether the graph $x^2+2xy-3y^2+5x+6y-100=0$ whether the graph is parabola, ellipse, or hyperbola?

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Answer 1 · 2018-02-01T10:47:51

Given: $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$
The discriminant is, $del=B^2-4AC$
If $del<0$ , then, if $B=0 and A=D$ , a circle. Otherwise, an ellipse.
If $del=0$ , then a parabola
If $del>0$ , then a hyperbola.

Explanation:

Given: $x^2+2xy-3y^2+5x+6y-100=0$

$A = 1$ , $B=2$ , and $C= -3$

$del = 2^2-4(1)(-3)$

$del = 16$ , then it is a hyperbola.

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How do use the discriminant test to determine whether the graph $x^2+2xy-3y^2+5x+6y-100=0$ whether the graph is parabola, ellipse, or hyperbola?

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How do use the discriminant test to determine whether the graph x^2+2xy-3y^2+5x+6y-100=0x^2+2xy-3y^2+5x+6y-100=0 whether the graph is parabola, ellipse, or hyperbola?

1 Answer

Explanation:

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How do use the discriminant test to determine whether the graph $x^2+2xy-3y^2+5x+6y-100=0$ whether the graph is parabola, ellipse, or hyperbola?