What happens if we keep $x$ and $y$ constant and change $\theta$ and $\rho$ in equation
$$x \cdot cos (\theta) + y \cdot sin (\theta) = \rho$$
I know the plot would look like a sine wave.
But, how would be the effect of $x$ and $y$ on the graph? What would be the relationship between (x, y) and the amplitude and phase of the wave?
I have plotted the equation using Wolfram Alpha. The plot doesn't make much sense.