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Hyperbola

Hyperbola. Warm Up: Try to recall the standard form of a hyperbola’s equation And use it to find the equation of a hyperbola with a center of (1, -1), a vertex of (3, -1) and a foci at (4, -1). Objective: Be able to get the equation of a hyperbola from given information or the graph

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Hyperbola

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  1. Hyperbola Warm Up: Try to recall the standard form of a hyperbola’s equation And use it to find the equation of a hyperbola with a center of (1, -1), a vertex of (3, -1) and a foci at (4, -1). Objective: Be able to get the equation of a hyperbola from given information or the graph Be able to find the key features of and graph a hyperbola Thinking Skill: Explicitly assess information and draw conclusions

  2. Hyperbola • Definition: A hyperbola is the set of all points (x, y) where the difference of the distances from two fixed points (foci) is constant • Equations • Horizontal – Vertical Asymptotes Asymptotes Where the center is (h, k), and a2 + b2 = c2

  3. Examples • Find the center, vertices, foci and asymptotes of then graph.

  4. Examples • Find the center, vertices, foci and asymptotes then graph

  5. Examples • Find the equation of the hyperbola with foci (-1, 2) and (5, 2) and vertices (0, 2) and (4, 2).

  6. Examples • Find the equation of the hyperbola with foci (10, 0) and (-10, 0) and asymptotes of y = ¾x and y = -¾x

  7. Two microphones, 1 mile apart, record an explosion. Microphone A receives the sound 2 seconds before microphone B. Find an equation representing where the explosion occurred.Note: 5280ft = 1mi & sound travels 1100ft/sec

  8. Closing Problem Find the standard form equation of the hyperbola with vertices of (-1, 3) & (-1, 9) and a focus of (-1, -1).

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