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Published byCecily Greer Modified over 3 years ago

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10.3 Hyperbolas

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Circle Ellipse Parabola Hyperbola Conic Sections See video!

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Where do hyperbolas occur?

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Hyperbolas Hyperbola: set of all points such that the difference of the distances from any point to the foci is constant. Difference of the distances: d 2 – d 1 = constant vertices The transverse axis is the line segment joining the vertices. The midpoint of the transverse axis is the center of the hyperbola.. asymptotes d1d1 d1d1 d2d2 d2d2

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Standard Equation of a Hyperbola (Center at Origin) This is the equation if the transverse axis is horizontal. (–a, 0)(a, 0) (0, b) (0, –b)

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Standard Equation of a Hyperbola (Center at Origin) This is the equation if the transverse axis is vertical. (0, –a) (0, a) (b, 0)(–b, 0)

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How do you graph a hyperbola? To graph a hyperbola, you need to know the center, the vertices, the fundamental rectangle, and the asymptotes. Draw a rectangle using +a and +b as the sides... (–4,0)(4, 0) (0, 3) (0,-3) a = 4 b = 3 The asymptotes intersect at the center of the hyperbola and pass through the corners of the fundamental rectangle Example: Graph the hyperbola Draw the asymptotes (diagonals of rectangle)... Draw the hyperbola...

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Example: Write the equation in standard form of 4x 2 – 16y 2 = 64. Find the vertices and then graph the hyperbola. Get the equation in standard form (make it equal to 1): 4x 2 – 16y 2 = 64 64 64 64 (–4,0)(4, 0) (0, 2) (0,-2) That means a = 4 b = 2 Vertices: Simplify...

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Standard Equations for Translated Hyperbolas

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