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Hyperbolas Chapter 8 Section 5
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Objective You will be able to differentiate between Horizontal and Vertical Hyperbolas and then be able to sketch a graphical representation of the equation.
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Vocabulary Hyperbolas: the set of all points in a plane such that the Absolute Value of the difference of the distances from two fixed points is constant. Foci (Plural of Focus): the two fixed points inside each hyperbolic section used to generate the graph.
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Vocabulary Center: midpoint of the distance between the 2 vertices of the hyperbola. Tranverse Axis: segment of length 2a whose endpoints are the vertices of the hyperbola. (~Major Axis) Conjugate Axis: segment of length 2b that is perpendicular to the transverse axis of the hyperbola at the center. (~Minor Axis) Asymptote: Lines which graph cannot touch or cross.
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Hyperbola This gives the Pythagorean equation c2 = a2 + b2. a = Leg
The hyperbolic equation is a difference of 2 squares so the Pythagorean is a sum. a = Leg (Distance from center to transverse vertex) b = Leg (Distance from center to conjugate vertex) c = Hypotenuse (distance from center to a focus.)
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Equations
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Table of Equations and important information
Equations of Hyperbolass centered at the Origin Standard Form Direction of Major Axis Horizontal Vertical Foci (h + c, k), (h - c, k) (h, k + c), (h, k - c) Transverse Vertices (h + a, k), (h - a, k) (h, k + a), (h, k - a) Conjugate Co-Vertices (h, k + b), (h, k - b) (h + b, k), (h - b, k) Equations of Hyperbolas centered at (h, k) Asymptotes
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Quick Clues The Denominator does not matter. The graph is Horizontal if the x2 is positive and the graph is Vertical if the y2 is positive.
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