Section 10 3 Hyperbolas 1 Objective By following

Section 10. 3 Hyperbolas 1

Objective By following instructions students will be able to: § Write equations of hyperbolas in standard form. 2 § Find asymptotes of hyperbolas. § Use properties of hyperbolas to solve real-life problems. § Classify conic sections from their general equations.

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Hyperbolas in Real life 4

Def: A hyperbola is the set of all points P in a plane such that the sum of the distances between P and two fixed points, called the foci, is a constant. y y x x

y y x x

EXAMPLE 1: Sketch the hyperbola given by. Identify the vertices, foci, and asymptotes. 7

EXAMPLE 2: Find the standard form of the equation of the hyperbola with foci at (-1, 2) and (5, 2) and vertices (0, 2) and (4, 2). 8

U-TRY #1 9 1) Graph the equation. Identify the vertices, foci, and asymptotes of the hyperbola. A) B) 1) Write an equation of the hyperbola with the given foci and vertices a) Foci (-3, 0), (3, 0); vertices (-1, 0) and (1, 0) b) Vertices (0, 2), (0, -2); foci (0, 4) and (0, -4) 9

EXAMPLE 3: Identify the conic section. Next, write the equation in standard form and sketch its graph. Label all of its parts. 10

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EXAMPLE 4: Classify each graph. a) b) c) d) 12

EXAMPLE 5: 13 Find the standard form of the equation of the hyperbola having vertices at (3, -5) and (3, 1) and with asymptotes y=2 x-8 and y=-2 x+4

EXAMPLE 6: Two microphones, 1 mile apart, record an explosion. Microphone A received the sound 2 seconds before microphone B. Where was the explosion? 14

U-TRY #2 Classify the conic section. A) B) C) D) 15

Revisit Objective Did we… § Write equations of hyperbolas in standard form? 16 § Find asymptotes of hyperbolas? § Use properties of hyperbolas to solve real-life problems? § Classify conic sections from their general equations?

Homework § Pg 720 #s 1 -35 ODD, 44 -51 ODD, 17