1
vote
2answers
36 views

Is equation for ellipse in polar coordinates correct?

Wikipedia gives the following equation for the conic sections in the polar coordinate system: $r = \frac{l}{1+e\cos\varphi}$. According to the article on conic sections, in case of an ellipse $e = ...
1
vote
1answer
68 views

Which conic is represented by $r = a \cos \theta$

The polar equation $r = a \cos \theta$ represents which conic?
0
votes
0answers
99 views

Polar equation of perimeter of half ellipse

x = Cx + a * cos(ang); y = Cy + b * sin(ang); Cx, Cy are cords of center. ...
0
votes
1answer
452 views

Hyperbola in polar coordinates, what's wrong?

I read that the equation of a conic in polar coordinates is $$r=\frac{l}{1+e\cos \theta}.$$ But when I try to reduce the hyperbola $$x^2 - y^2 =1$$ to that form by setting $x=r\cos \theta $, $y=r ...
3
votes
2answers
13k views

Ellipse in polar coordinates

I think Wikipedia's polar coordinate elliptical equation isn't correct. Here is my explanation: Imagine constants $a$ and $b$ in this format - Where $2a$ is the total height of the ellipse and $2b$ ...
1
vote
1answer
124 views

Problem with ellipse equation

How one get from this ellipse equation $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$ that ellipse equation $$\frac{x^2+y^2}{F(\phi)^2}=1,$$ where $$F(\phi)=\frac{ab}{\sqrt{(b\cos\phi)^2+(a\sin\phi)^2}}$$ and ...
1
vote
0answers
227 views

(Calculus 3) Having trouble finding the polar equation of a hyperbola.

Eccentricity e=sqrt(2), and one vertex is located at (2,0). I do know that if the vertex is located at (2,0), then the directrix is 2 units from the vertex. I am not sure how to find the location of ...
1
vote
2answers
4k views

Set up double integral of ellipse in polar coordinates?

How do you set up a double integral for an ellipse in polar coordinates without using Jacobian or Greens Theorem? I can't seem to figure out what (or if) the limits of r can possible be. $x = ...