Rotated ellipse equation sought
I'm looking for a Cartesian equation for a rotated ellipse.
h is x-koordinate of the center of the ellipse.
k is y-koordinate of the center of the ellipse.
a is the ellipse axis which is parallell to the x-axis when rotation is zero.
b is the ellipse axis which is parallell to the y-axis when rotation is zero.
phi is the rotation angle.
Here is a cartesian equation for a non-rotated ellipse:
(How do I "put rotation phi" into this?)
------- + ------- = 1
Here is a parametric form of a rotated ellipse:
x = h+a*cos(t)*cos(phi)-b*sin(t)*sin(phi)
y = k+b*sin(t)*cos(phi)+a*cos(t)*sin(phi)
I'd like to have the x and the y in the same equation, and without the parameter t. I think that this means that I want a Cartesian equation for a rotated ellipse, but I'm sorry if I have misunderstood Cartesian here...
Thanks beforehand and a jolly good weekend to ya' all!