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

  1. Jan 19, 2012 #1
    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.
     
  2. jcsd
  3. Jan 19, 2012 #2
    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].
     
  4. Jan 19, 2012 #3
    Re: Length of a line segment that binds the center of an ellipse with point of the el

    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.
     
  5. Jan 19, 2012 #4
    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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