For an ellipse with the equation $$\frac{(x-\tfrac{1}{3})^2}{\tfrac{4}{9}}+\frac{y^2}{\tfrac{1}{3}}=1\;,$$ at what point does the reflected beam cross the x axis if a ray of light is emitted from the origin at an angle of $\frac{\pi}{6}$ to the $x$ axis.
I have attempted to begin this by working out a tangent line but has not helped me.