Checking a Polar Equation of a Conic

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In summary, the homework statement is asking if the homework was done correctly. The student has plotted a parabola with a directorix at x=3 and found that r=-3/ (1-cos(θ)) which is similar to their equation. They also found that the parabola is oriented with the +x axis and has the focus at the origin. They checked off what they were asked to and wrote down a similar list to what they had before.
  • #1
Jbreezy
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Homework Statement


I want to know if I did these right.

Write a polar equation of a conic with the focus at the origin and the given data.

Homework Equations



r = (ed) /(1+- cos(theta)) and r = r = (ed) /(1+- sin(theta))


The Attempt at a Solution



Parabola , directrix x = -3 I came up with r = -3/ (1 -cos(θ))

Hyperbola, eccentricity 3, directrix x = 3
I got 9/(1+3cos(θ))

What do you think OK?
 
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  • #2
Did you try plotting them?
For instance, a parabola with directorix -3 ... what would a sketch of it look like?
Does this match up with some values - like what would r be at zero angle?
Does that match up with your equation?
 
  • #3
Yeah I plotted them. Idk tho
 
  • #4
Yeah I plotted them.
And? ... what did you find out?

Idk tho
Idk <looks it up> "I don't know"?
What don't you know?

Tho <looks it up>
1. From Middle English tho, tha, from Old English þā (“the, those”, plural), from Proto-Germanic *þai (“those”), from Proto-Indo-European *to-, *só (“that”).
2. abbv. Thor Industries
3. Internet slang - short for "though"
<sigh>

If you were to sketch a parabola with a directorix at x=3,
- is the parabola oriented with the +y axis? The +x axis? something else?
- where is the focus?
- what sort of value should r have at easy angles like 0, 90, 180, 360?
- will r ever be negative?

How does this compare with the results fro your equation: ##r=-3/(1-\cos\theta )## ?

If you don't know the basic properties of a parabola, without using the equation, then you need to learn them.
http://en.wikipedia.org/wiki/Conic_section
 
Last edited:
  • #5
Hyperbola, eccentricity 3, directrix x = 3
I got 9/(1+3cos(θ)) This one is to the right. The some. The question say's " Write a polar eq. of a conic with the focus at the origin and the given data".
So, this one OK?
 
  • #6
Well ... write down a similar list to before and check it off.
What do you get?
 
  • #7
Well ... write down a similar list to before and check it off.
What do you get?
 

Related to Checking a Polar Equation of a Conic

1. What are the key components of a polar equation of a conic?

The key components of a polar equation of a conic are the focus, the directrix, and the eccentricity. These elements determine the shape and orientation of the conic section.

2. How do you check if a polar equation represents a circle?

To check if a polar equation represents a circle, you can rewrite it in the form r = a, where 'a' is a constant. If this is the case, then the equation represents a circle with radius a centered at the origin.

3. What is the method for determining if a polar equation represents an ellipse or a hyperbola?

The method for determining if a polar equation represents an ellipse or a hyperbola is to rewrite it in the form r = (ed) / (1 ± e cos θ), where 'e' is the eccentricity and 'd' is the distance from the focus to the directrix. If 'e' is less than 1, the equation represents an ellipse. If 'e' is greater than 1, the equation represents a hyperbola.

4. How can you tell if a polar equation represents a parabola?

A polar equation represents a parabola if it can be rewritten in the form r = (1 + cos θ) / (1 - e cos θ), where 'e' is the eccentricity. The parabola will have a focus at the origin and its directrix will be perpendicular to the polar axis, passing through the focus.

5. What is the process for graphing a polar equation of a conic?

To graph a polar equation of a conic, you can use a polar graphing calculator or plot points by hand. First, determine the key components of the conic (focus, directrix, and eccentricity). Then, plug in various values of θ and solve for r to plot points on a polar coordinate plane. Finally, connect the points to get a visual representation of the conic section.

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