April 26, 2016
GETTING STARTED
1. Please have your homework out.
2. Chapter 10 Test Friday.
3. Any questions??? Put a tally...
40.
50.
42.
53.
44.
56.
59.
April 26, 2016
April 26, 2016
10.4 Hyperbola Extensions Day 1
A hyperbola is the set of all points (x,y) the difference of whose distances
from two distinct fixed points (foci) is a positive constant.
d2
• What is the constant distance in terms of a, b, c?
• What if we put the point (x,y) on the transverse
axis (i.e. at a vertex)???
Focus
(x,y)
Focus
April 26, 2016
Cool fact about hyperbolas...
• Imagine that two guns
are fired at point S and
point M.
• The sound waves from
these two gun shots will
intersect in the shape of
a hyperbolas!!!
Cool fact about hyperbolas...An example
• There are 2 microphones, M1 and M2.
• A gun is shot at point S.
• M1 records the gun shot 1 second after M2.
• Because sound travels at 1100 feet per
second, M1 is 1100 feet further from S than M2.
We don't know where S is, but will this difference
in distance be a constant? Why is this
significant?
***YES!
***Therefore, we can model this using
a hyperbola (constant difference
between two foci)!
April 26, 2016
April 26, 2016
Ex 1) Suppose that two people standing 1 mile apart see a flash
of lightning. After a period of time, the person standing at point A
hears the thunder. One second later, the person standing at point
B hears the thunder. If the person at B is due west of the person
at A and the lightning strike is known to occur due north of the
person standing at A, where did the lightning strike???
Ex 2) Some nuclear power plants are in the shape of a hyperboloid, a solid obtained
by rotating a hyperbola about its conjugate axis (i.e. not the transverse axis). Suppose
such a cooling tower has a base diameter of 200 feet and the radius at its narrowest point,
180 feet above the ground, is 50 feet. If the radius at the top of the tower is 75 feet,
how tall is the tower?
April 26, 2016
HW
Finish WS
April 26, 2016
Ex 2) Suppose that two people standing 2 miles apart both see the burst
from a fireworks display. After a period of time, the first person standing
at point A hears the burst. One second later, the second person standing at
point B hears the burst. If the person at point B is due west of the person at
point A and if the display is known to occur due north of the person at
point A, where did the fireworks display occur?