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10.3 Hyperbolas

10.3 Hyperbolas. Conic Sections. See video!. Circle Ellipse. Parabola Hyperbola. Where do hyperbolas occur?. Hyperbolas. Difference of the distances: d 2 – d 1 = constant. d 2. d 1. vertices. d 1. d 2.

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10.3 Hyperbolas

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  1. 10.3 Hyperbolas

  2. Conic Sections See video! Circle Ellipse Parabola Hyperbola

  3. Where do hyperbolas occur?

  4. Hyperbolas Difference of the distances: d2 – d1 = constant d2 d1 vertices d1 d2 Hyperbola: set of all points such that the difference of the distances from any point to the foci is constant. asymptotes The transverse axis is the line segment joining the vertices. The midpoint of the transverse axis is the center of the hyperbola..

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

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

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

  8. Get the equation in standard form (make it equal to 1): 4x2 – 16y2 = 6464 64 64 Simplify... Example: Write the equation in standard form of 4x2 – 16y2 = 64. Find the vertices and then graph the hyperbola. That means a = 4b = 2 Vertices: (0, 2) (–4,0) (4, 0) (0,-2)

  9. Standard Equations for Translated Hyperbolas

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