x = Cx + a * cos(ang);

y = Cy + b * sin(ang);

Cx, Cy are cords of center. ang is angle in radians. a is half of width, b is half of height.

If I change values of ang, I get different points on circumference of ellipse. Below is the path which I get with above equation.


But instead of this elliptical shape, I want something like half ellipse, something like concave mirror. Even if we stretch both of its end to infinity, they should not form elliptical shape.


Can somebody provide me polar equations for second curve. I am very bad at digital drawing but you can imagine thas as concave mirror.

  • $\begingroup$ Did you obtain the entire ellipse by a suitable command or by a loop drawing concatenated segments ? $\endgroup$ – Tony Piccolo Oct 12 '13 at 11:29
  • $\begingroup$ Actually, it's an equation of coordinates, if I change the angles, I'll get points on perimeter of ellipse. $\endgroup$ – Jashwant Oct 12 '13 at 11:56
  • $\begingroup$ The point is that polar equations for half an ellipse do not exist. One uses the same equations with a different range of the angle. Which software are you using ? I think you should edit to give an example of your operating. $\endgroup$ – Tony Piccolo Oct 12 '13 at 13:56
  • $\begingroup$ I am using javascript and I want to move a point from bottom to top and I do not want the point to loop back to bottom. May be I need an equation for parabola which looks like half ellipse ? :O $\endgroup$ – Jashwant Oct 13 '13 at 5:13
  • $\begingroup$ Sure ! Around every vertex, an ellipse is essentially a parabola. Because of this fact, the motion of a projectile near the earth is parabolic in spite of Kepler's first law. $\endgroup$ – Tony Piccolo Oct 13 '13 at 10:31

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