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

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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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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 [itex]a[/itex] and minor axis [itex]b[/itex], so that the equation of the ellipse in Cartesian coordinates is [itex](\frac{x}{a})^2+(\frac{y}{b})^2=1[/itex]. I take it you want to find the equation of the ellipse in polar coordinates, i.e. find [itex]r[/itex] as a function of [itex]\theta[/itex]. In that case, just do what you always do to convert to polar coordinates: plug in [itex]x=r\cos\theta[/itex] and [itex]y=r\sin\theta[/itex].
 
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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 [itex]a[/itex] and minor axis [itex]b[/itex], so that the equation of the ellipse in Cartesian coordinates is [itex](\frac{x}{a})^2+(\frac{y}{b})^2=1[/itex]. I take it you want to find the equation of the ellipse in polar coordinates, i.e. find [itex]r[/itex] as a function of [itex]\theta[/itex]. In that case, just do what you always do to convert to polar coordinates: plug in [itex]x=r\cos\theta[/itex] and [itex]y=r\sin\theta[/itex].
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.
 
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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 [itex]x[/itex] and [itex]y[/itex] axes (these are just the [itex]x[/itex] and [itex]y[/itex] coordinates, after all). On the other hand, polar coordinates specify the distance from the origin (called [itex]r[/itex], as in radius) and the angle that the line through the point makes with the [itex]x[/itex] axis (usually denoted by [itex]\theta[/itex]). 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 [itex]x[/itex] and [itex]y[/itex] in terms of [itex]r[/itex] and [itex]\theta[/itex].

250px-Polar_to_cartesian.svg.png


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).
 

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