Use the Discriminant to Determine If the Graph of the Equation

question 54

Essay

Use the discriminant to determine if the graph of the equation, $16 x ^ { 2 } - 24 x y + 9 y ^ { 2 } - 60 x - 80 y = 0$ 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:

Age Of Majority

The legally recognized age at which an individual is considered an adult and capable of making decisions and entering into contracts without parental consent.

Reasonable Period

Refers to a time frame that is considered fair and appropriate under the circumstances to perform a certain task or fulfill an obligation.

Disaffirm Contracts

The legal ability of one party, often a minor or someone not fully competent, to declare a contract void and release themselves from any contractual obligations.

Necessaries

Goods or services that are essential for maintaining a person's health, education, comfort, or welfare.