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Need help on ellipse equation

  1. Jan 3, 2012 #1
    Hi, guys,

    Is the ellipse equation "x=acost; y=bcost" a Cartesian coordinates equation or a polar coordinates equation? Someone said that it's a transfer from a polar one to a Cartesian one.
    Need more help on this, thank you very much!
  2. jcsd
  3. Jan 3, 2012 #2
    Cartesian I think as you get x and y axis coordinates.
  4. Jan 3, 2012 #3
  5. Jan 3, 2012 #4
    You did mean [itex]x=a\cos(t),~~y=b\sin(t)[/itex], right?
  6. Jan 4, 2012 #5


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    These are parametric equations giving Cartesian coordinates. If you really mean x= a cos(t), y= b cos(t), you can solve the first equation as cos(t)= x/a so the second equation becomes y= (b/a)x, which graphs as a straight line.

    If you meant x= a cos(t), y= b sin(t), as micromass suggests, then x/a= cos(t), y/b= sin(t) so that [itex](x/a)^2+ (y/b)^2= cos^2(t)+ sin^2(t)= 1[/itex], an ellipse.

    The equations relating polar coordinates and Cartesian coordinates are different but similar: [itex]x= r cos(\theta)[/itex], [itex]y= r sin(\theta)[/itex].
  7. Jan 8, 2012 #6
    Thank you very much, guys.
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