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Hyperbola

Recall standard hyperbola equations to find equation with center (1, -1), vertex (3, -1), and foci (4, -1). Learn to derive and graph a hyperbola from given data, assess information accurately, and draw conclusions. Dive into hyperbola definitions, equations, asymptotes, and examples. Practice finding vertices, foci, asymptotes, and graphing the hyperbola. Solve problems like locating an explosion using sound data. Conclude with finding the equation for a hyperbola given specific vertex and focus coordinates.

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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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