[Math] Find angle at given points in Ellipse

Question

I have Ellipse's center-points, minor-radius and major-radius.

I can find, how to check if given point(x, y) exists in Ellipse or not.

Now, I want to find given point(x,y) exists at which angle in Ellipse.

Thanks in advance
Vikram

Answer 1

Taking the answer of mathlove $x=acosθ, y=bsinθ$ you can derive using that $tan:=sin/cos$ this formula:

$y = b \ cosθ \ tanθ;$ with $cosθ =$ $x \over a;$

=> $y =$ $b \over a$ $x \ tanθ;$

=> $θ =$ $atan($$y \over x$$a \over b$$)$