Section 10.3 Hyperbolas

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

Hyperbolas in Real life

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. x y

x y

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

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).

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

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

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

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

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

Homework Pg 720 #s1-35 ODD, 44-51 ODD,