Are You Eccentric, Angle?

The normal lines to $4x^2+9y^2=36$ at $A(\theta_1)$ , $B(\theta_2)$ , $C(\theta_3)$ and $D(\theta_4)$ are concurrent at $P$ .

Now, the points $A, \ B, \ C$ and $D$ satisfy the condition $\sum_{i=1}^{4} \cos{\theta_i}-\sin{\theta_i}=0$

The point $P$ must lie on

Note : $\theta_i$ are the Eccentric Angles of the respective points.