Use the Discriminant to Determine If the Graph of the Equation

question 70

Essay

Use the discriminant to determine if the graph of the equation, $3 x ^ { 2 } + 10 x y + 3 y ^ { 2 } + 8 = 0$ is a parabola, an ellipse or a hyperbola, then use a rotation of axes to eliminate the $x y$ - term, and sketch the graph.

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Definitions:

Fallacy Of Accident

A logical error that occurs when an argument mistakenly applies a general rule to a specific case that is exceptional or atypical.

Rule Of Thumb

A practical and approximate way of doing or measuring something, based on experience rather than exact calculations.

Hasty Generalization

A logical fallacy where a conclusion is reached on the basis of insufficient evidence, generalizing too quickly from too little information.

Composition

The fallacy of inferring that a whole has a property merely because its parts have that property.