# Eccentric Ellipse

**Geometry**Level 2

The tangent at \(P(\phi)\) of the ellipse \(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1\) meets its auxiliary circle at points \(Q\) and \(R\). If the chord \(QR\) subtends a right angle at the origin, find the value of:

\[e\sqrt{1+\sin^2 \phi} \]

**Details and Assumptions**

- Assume \(a > b\)
- \(P(\phi)\) refers to the point \(P(a \cos \phi, b\sin \phi)\), where \(\phi\) is the eccentric angle
- The auxiliary circle of the ellipse \(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1\) is \(x^2+y^2=a^2\)