So for a Algebra 2 project I'm supposed to create a figure with functions and circles. I want to recreate a face with ellipses acting as the eyes. The character I'm trying to recreate, Butters from South Park, has eyes that are ellipses but are rotated slightly. I have the 2 equations for each of the eyes: $$\frac{\left(\left(x-2.5\right)\cos\left(2\right)+\left(y\right)\sin\left(2\right)\right)^2}{\left(17\right)}+\frac{\left(\left(x+1.24328907\right)\sin\left(2\right)-\left(y\right)\cos\left(2\right)\right)^2}{\left(9\right)}=1$$
$$\frac{\left(\left(x+12\right)\cos\left(-2\right)+\left(y-1\right)\sin\left(-2\right)\right)^2}{\left(17\right)}+\frac{\left(\left(x+6\right)\sin\left(-2\right)-\left(y-1\right)\cos\left(-2\right)\right)^2}{\left(9\right)}=1$$
Part of the instructions is to the equations into y= format. For a normal ellipse you can use the equation in y= as: $$y=b\sqrt{1-\frac{x-h}a}+k$$ so what would the equation of a rotated ellipse be in the rotated from involving sin and cos? Thanks