Filtered Curve vs. Original (Part 3)

Two discrete curves are defined as follows:

$\Delta \theta = \frac{\pi}{1000} \\ \alpha = 0.995 \\ k = 0,1,2,3 .... 1000 \\ \theta_k = k \, \Delta \theta \\ x_k = \cos(\theta_k) \\ y_k = \sin(\theta_k) \\ y'_k = \alpha \, y'_{k-1} + (1 - \alpha) y_k \\ y'_0 = 0$

Scatter plots of $(x_k,y_k)$ and $(x_k,y'_k)$ are shown as smooth lines for display purposes.

The $k$ subscript denotes the present value of the variable, and the $k-1$ subscript denotes the previous value of the variable. The quantity $y'$ is the result when $y$ is passed through an infinite-impulse-response filter.

What is the ratio of the blue-shaded area to the tan-shaded area?