# Messed Up

**Geometry**Level pending

In an orthonormal system \((O; \vec u; \vec v ) \), consider \(M(x,y) \) moving on \((E)\): \(25(x^2+y^2) = (3x-16)^2 \) having a directrix \((D) \): \(x = \dfrac{16}3 \). Let \( ( \vec u ; \vec{OM} ) = \theta \). \((OM) \) meets \((E) \) at \(M' \).

Given that \( \dfrac1{OM} + \dfrac1{OM'} = \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).