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Conic Classification
Classification of Quadratic Type Functions by Type of Conic Section
5
Mathematics
Undergraduate 1
10/10/2013

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Term
Parabola (there is only one quadratic term, and it involves x or y but not both)
Definition
What type of conic section is x = 12*y2 (12 y squared)?
Term
Circle (there is a quadratic term involving x and a quadratic term involving y, and the coefficient of those terms are the same)
Definition
What type of conic section is x2 + 2x + y2 - 16y = 16 (x2 means "x squared" and y2 means "y squared")?
Term
Ellipse (there is a quadratic term involving x and a quadratic term involving y, and the coefficient of those terms are the different but the same sign)
Definition
What type of conic section is x2 - 4x + 3y2 + 15x = 7 (x2 means "x squared" and y2 means "y squared")?
Term
Hyperbola (there is a quadratic term involving x and a quadratic term y, and the coefficients of those terms have different signs
Definition
What type of conic section is 10x2 - 20y2 = 80 (x2 means "x squared" and y2 means "y squared")
Term
Hyperbola (any conic section with equation xy = k is a hyperbola)
Definition
What type of conic section is xy = 12, or y = 12/x?
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