10.5, Day #1 Hyperbolas!. Do Now Earn 10 Team Challenge Points For Your Group if You Are the First to Get This There are three working switches downstairs.

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Presentation transcript:

10.5, Day #1 Hyperbolas!

Do Now Earn 10 Team Challenge Points For Your Group if You Are the First to Get This There are three working switches downstairs. Each corresponds to one of the three light bulbs in the attic. You can turn the switches on and off and leave them in any position. You cannot recruit help. How would you identify which switch corresponds to which light bulb, if you are only allowed one trip upstairs?

Keep the first bulb switched on for a few minutes. It gets warm, right? So all you have to do then is... switch it off, switch another one on, walk into the room with bulbs, touch them and tell which one was switched on as the first one (the warm one) and the others can be easily identified...

Where We Are and Where We Are Going Tuesday and Wednesday (12/13 and 12/14): Hyperbolas Thursday and Friday (12/15 and 12/16): Parabolas Gone Wild! Monday (12/19): 10.2, 10.5 Review Tuesday (12/20): 10.2, 10.5 Quiz Wednesday (12/21): Classifying Conics Thursday and Friday (12/22 and 12/23): Quadratic Systems Then—Bye Bye, Winter Break

Hyperbolas

Hyperbolas!

A hyperbola has some applications in science. It is used for example 1. To track particles in particle physics 2. Gas properties including Boyle's Law, Charles' Law, Ideal Gas Law, etc. 3. For designing lens 4. For analyzing capillary forces 5. For studying some comets

a = distance from midpoint (center) to the vertex along the transverse axis. b = distance from midpoint (center) along the perpendicular segment called the conjugate axis. c = distance from midpoint to the focus (which is on the transverse axis). Fun Facts a.The numerators switch. (Denominators switched for ellipses) b.b can be > than a for hyperbolas.

If I were a function you would be my asymptote - I always tend towards you.

Give it a go! Graph. Identify center, vertices, co-vertices, foci, and asymptotes. 18y 2 -2x 2 =72 Center: Vertices: Co-vertices: Foci: Asymptotes:

Equations of Hyperbolas Write the equation of the hyperbola. Identify the asymptotes. Given foci (0, -3) and (0, 3) and Vertices (0, -2) and (0, 2)

Center: Vertices: Co-vertices: Foci: Asymptotes: Length transverse axis:

Write in Standard Form

Application