Re: two little angel/degrees graphing questions

On Fri, 10 Jun 2005, Alfred Z. Newmane wrote:

> First off I want to confirm I've got it right this far:
>
> 0 Degrees (with origin (0, 0)) ends up, from (0, 0), pointing East,
> 90 Degrees (with origin (0, 0)) ends up, from (0, 0), pointing North,
> 180 Degrees (with origin (0, 0)) ends up, from (0, 0), pointing West,
> and
> 270 Degrees (with origin (0, 0)) ends up, from (0, 0), pointing South.
>
Yes, this seems like an apt visualization tho traditionally one would
state that at 0 degrees from the positive x-axis (conventionally in the
counter clockwise direction) and a distance 1 from the origin, is the
point (0,1)

> Thats what I get using
> Cos(Angle) * Radius = X
> to get the X coord and
> Sin(Angle) * Radius = Y
> to get the Y coord.
>
Ok, parametric equations of the circle.

> This works fine for a circle, as the radius is the same all around.
>
> But what about an ellipse?
>
> First I need to figure out what the radius is for a given point?
>
Ellipses don't have a radius or diameter, they have a major and minor
axis. Equation of ellipse, centered at (0,0) with axis along the x and y
axis of length 2a and 2b is
(x/a)^2 + (y/b)^2 = 1,
which is the same as for the circle when a = b.

The parametric equations for the same are
x = a.cos t
y = b.cos t

> Heres what I know abotu the ellipse:
>
> - I know the width and height.

The width and height are the length of the axis.

> How can I get the radius of an ellipse at a given angle?
>
Ellipses don't have a radius. This distance to the ellipse
from the center is
sqr(x^2 + y^2)
for the ellipse parametrized above computed for t = given angle.
.

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