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How does the eccentricity determine the type of conic section?...

Question

How does the eccentricity determine the type of conic section?

How does the eccentricity determine the type of conic section?



Answers

Explain how eccentricity determines which conic section is given.

So we're being asked, What do we know about the focus or the folk I of a comic section? It is written as a polar equation. If a Connick section, Israel and polar Form than the iconic section will be located, the focus will be located at the origin. So that is what the answer to the question is the focus will be located at the origin.

Okay, were asked to explain how eccentricity determines rich Connick session is given. Now there's three big pieces. When it comes to comic sections, you've got the focus. You got the direct tricks and you've got a point on the graph. Now the eccentricity is just a ratio. Is the ratio of this length pdf in this length? P. Diddy? So if it happens that pdf is the same as P. Diddy, then no matter what they are, when you divide them, you're going to get one. We're right, one here. And if that happens, then you've got a parabola. Distance from pdf is always the same. It's distant impunity. No matter where you go along this line, it's always gonna be seem to get this nice equilibrium kind of just coast along here in both directions. That's a problem. But what if the distance from pdf is less than the distance from PBB? Well, then you're actually gonna get an ex interest. The lesson one, and it'll kind of like as it goes along, curl back in because Peter F is less than beauty and then come back around. That's in the lips. Of course, this is still bigger than zero. The last option is if Pdf is greater than P. Diddy. If that happens and as it goes longest, get further from away and then it comes goes off wildly into infinity. And that's how you get a high proble. So that's if E is greater than one. Or if the distance from P F is greater than the distance from P. Diddy. So eccentricity tells us which comic sections it is because it's letting us know the ratio between the PdF and Peavy telling us is the graph gonna be proble in the lips or high purple?

If the Connick isn't polar form, what do we know about the focus? Well, because of the way that polar form works where you started the center and you kind of circle out the origin is always gonna be the focus. So if it's in polar form, we know that the focus has to be at the origin.

So if we call f A fixed point and we call that the focus and then we call D a fixed line, which we call the direct tricks in a plane than a Connick, is the set of all points. P in a plane accepts that P f over P D is equal to e with e being a fixed positive number called the East Interesting.


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