# Length of a line segment that binds the center of an ellipse with point of the elipse

#### 32l3n

Hello to everyone!
I am really desparately trying to find the lenght of the "radius" of an ellipse.I will explain exactly what I mean by that - its the lenght of the line segment that connects the center of a particular ellipse with a given point of the same ellipse.All the information I have to solve this problem is the ellipse equation and an angle measured from the major axis to that line segment,the center of the ellipse and cartesian coordinate system .
All kinds of tips and hints will be greatly appreciated.

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#### A. Bahat

Re: Length of a line segment that binds the center of an ellipse with point of the el

Well, suppose (for simplicity) that the ellipse is centered at the origin and has major axis $a$ and minor axis $b$, so that the equation of the ellipse in Cartesian coordinates is $(\frac{x}{a})^2+(\frac{y}{b})^2=1$. I take it you want to find the equation of the ellipse in polar coordinates, i.e. find $r$ as a function of $\theta$. In that case, just do what you always do to convert to polar coordinates: plug in $x=r\cos\theta$ and $y=r\sin\theta$.

#### 32l3n

Re: Length of a line segment that binds the center of an ellipse with point of the el

Well, suppose (for simplicity) that the ellipse is centered at the origin and has major axis $a$ and minor axis $b$, so that the equation of the ellipse in Cartesian coordinates is $(\frac{x}{a})^2+(\frac{y}{b})^2=1$. I take it you want to find the equation of the ellipse in polar coordinates, i.e. find $r$ as a function of $\theta$. In that case, just do what you always do to convert to polar coordinates: plug in $x=r\cos\theta$ and $y=r\sin\theta$.
Thank you for the detailed answer, A.Bahat.It looks like this will solve the mystery.I don't understand the polar coordinate system and thats why I skiped this as an option.As I understand this polar equation represents a vector with a beginning the center of the Ellipse and an arrow which points at a specific fragment of the ellipse depending on the angle.

#### A. Bahat

Re: Length of a line segment that binds the center of an ellipse with point of the el

That's a pretty good way to put it. The Cartesian coordinates give you the horizontal and vertical distances from the $x$ and $y$ axes (these are just the $x$ and $y$ coordinates, after all). On the other hand, polar coordinates specify the distance from the origin (called $r$, as in radius) and the angle that the line through the point makes with the $x$ axis (usually denoted by $\theta$). It is pretty easy to go back and forth between these coordinate systems using some trigonometry. This picture shows how one finds the formulas I gave in the last post for $x$ and $y$ in terms of $r$ and $\theta$. That's really all there is to polar coordinates (along with converting polar coordinates to Cartesian coordinates, but that doesn't have anything to do with your question).