1. Section 10.3
Hyperbolas

2. 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.

4. Hyperbolas in Real life

5. 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

6. x y

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

8. 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).

9. 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

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

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

13. 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

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

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

16. 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?

17. Homework
Pg 720 #s1-35 ODD, ODD,