Hyperbola 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 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).

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

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

Examples Find the center, vertices, foci and asymptotes then graph

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

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

Two microphones, 1 mile apart, record an explosion 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

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