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?)**

Code:

`(x-h)^2 (y-k)^2`

------- + ------- = 1

a^2 b^2

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!

Cheers!