Hyperbolas

1
Hyperbolas

• By Selina, Ellen and Emma

2
Introduction

• Hyperbolas can be found in
• Astrophysics, e.g. Comet Paths
• Gear design
• Navigation
• Telescopic lenses
• Aerodynamics
• Power plants
• Radio waves
• Nature, e.g. Water ripples

3
Conic Sections

• Hyperbolas are one of four kinds of conic
  sections.
• All heavenly bodies move in conic sections
  ellipses, parabolas, hyperbolas and circles.

4
Comet Paths

• Most comets travel around the Sun in elliptical
  or open-ended parabolic and hyperbolic orbits.
• This means that they can appear anywhere
  in the sky.

5
Sonic BOOMS!

• When a plane goes at the speed of sound it
  creates a sonic boom shock wave in the shape of a
  cone.
• As it hits the ground it is intersected at 180
  degrees forming a hyperbola.

6
Radio waves and Navigation

• Radio waves and hyperbolas can be used in
  navigation.
• If the centre of each circle gives out a radio
  signal then the signals will intersect each other
  in hyperbolas.
• This is how hyperbolic radio navigation systems
  were created.

7
Ripples
This type of intersection can be seen in
nature. Next time you are near a pond throw two
pebbles into it next to each other and watch the
ripples. Where the circular waves intersect a
hyperbola is formed.
8
So what is a hyperbola?

• A hyperbola is a conic intersection with the
  following equation.

9
Conclusion

• So now you know!
• Go have a look around for hyperbolas wherever you
  can yourselves!
• Keep an eye out!
• Thanks for listening