What is the directrix for a polar conic with the given equation?

In summary, the conversation is about finding the directrix for a given equation. The attempt at a solution involves factoring the denominator and using the values of e and d to find the correct answer. However, the values used do not make sense and the person is advised to work on the entire fraction and use proper grammar when writing mathematical sentences.
  • #1
Jbreezy
582
0

Homework Statement



Hi wondering what the directrix is for this

Homework Equations



r = (20)/ (2+sin(theta))

The Attempt at a Solution



I factored denominator so it read 2(1+ (1/2)sin(theta)) ...So I said e times d = (2/20) and I got d = (1/5) because e is (1/2). Doesn't make sense though seems to small because that lies inside of the thing when I graph it.
 
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  • #2
I factored denominator so it read 2(1+ (1/2)sin(theta)) ...So I said e times d = (2/20) and I got d = (1/5) because e is (1/2). Doesn't make sense though seems to small because that lies inside of the thing when I graph it.

This bit you did OK - try working on the whole fraction though.
$$r=\frac{20}{2+\sin\theta} = \frac{10}{1+\frac{1}{2}\sin\theta}=\frac{ed}{1+e\sin\theta}$$

So ##e=\frac{1}{2}## right? And ##ed=\cdots##?
 
  • #3
d = 20? ed = 10 = (1/2) = 10
 
  • #4
Jbreezy said:
d = 20? ed = 10 = (1/2) = 10
Um... that is just nonsense. eg. 10 ≠ (1/2)

You have to use reasonable grammar when you write sentences in any language.
Math is also a language - therefore you should take some trouble to make sure the math/number sentences you write down actually mean something.

Want to try again?
 

Related to What is the directrix for a polar conic with the given equation?

1. What are the parameters for polar conics?

The parameters for polar conics include the eccentricity, the semi-major axis, the semi-minor axis, the orientation angle, and the position of the focus point.

2. How do you calculate the eccentricity for a polar conic?

The eccentricity is calculated by taking the distance between the center and the focus point and dividing it by the distance between the center and the directrix.

3. What is the significance of the semi-major and semi-minor axes in polar conics?

The semi-major and semi-minor axes determine the shape and size of the polar conic. The semi-major axis is the distance from the center to the farthest point on the conic, while the semi-minor axis is the distance from the center to the nearest point on the conic.

4. How does the orientation angle affect a polar conic?

The orientation angle determines the rotation of the conic about its center. A change in the orientation angle will result in a different orientation and shape of the conic.

5. What is the role of the focus point in a polar conic?

The focus point is a fixed point that determines the shape of the polar conic. The distance between the focus point and any point on the conic is equal to the distance between the focus point and the directrix.

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