How do use the discriminant test to determine whether the graph 4xy+5x10y+1=0 whether the graph is parabola, ellipse, or hyperbola?

1 Answer
Dec 22, 2016

Please see the explanation.

Explanation:

Here is a reference Conic Sections that I will use.

Here is the general Cartesian form of a conic section:

Ax2+Bxy+Cy2+Dx+Ey+F=0

The discriminant is: B24AC

The discriminant test is the following 3 "If-then" tests; two of which have subordinate special cases:

[1] If B24AC<0, then the equation represents an ellipse.

[1.1] A subordinate special case of this occurs when A=CandB=0, then the equation represents a circle.

[2] If B24AC=0, then the equation represents a parabola.

[3] If B24AC>0, then the equation represents a hyperbola.

[3.1] A subordinate special case of this occurs, when A+C=0, then the equation represents a rectangular hyperbola.

The given equation is the type specified by [3.1]. A rectangular hyperbola .

Here is the graph of the equation:

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