Are You Eccentric, Angle?

Geometry Level 5

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.

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