7.5 Conic Sections

[STARTS AT 27:45]

Instructor: All right, so identify and create the graph of the conic section described by this equation. So first off, the major axis is horizontal here, all right? And I know that ep, eccentricity times the focal parameter is 3 because of our numerator. 

And I know that my eccentricity is 2 because of what's in the denominator. Putting those two together means that my p is 3/2. My focal parameter is 3/2. And because my eccentricity is greater than 1, this is a hyperbola, all right? So I can tell you that. It's a hyperbola, and my focal parameter is 3/2. 

So let's look at a graph and table for this function. All right, so here's my table. My theta is at theta equal to 0. My radius is 1. 

At pi over 4, my radius is 1.24. Let's put it right there, OK. Pi over 2, I have a radius of 3. And 3 pi over 4 my radius is negative 7, which means it's going to be way out here. OK? 

At pi, my radius is negative 3. At 5 pi over 4, my radius is negative 7, which means it's off in that direction. 3 pi over 2, my radius is 3. And 7 pi over 4, a radius of 1.2. 

Now, you probably can't see this very well. But what happens here, our center appears to be this point right here where r equals 2. And it looks like this.

[ENDS AT 30:20]