8 The diagram shows the ellipse \(E\) with equation $$\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 4 } = 1$$ and the straight line \(L\) with equation $$y = x + 4$$ \includegraphics[max width=\textwidth, alt={}, center]{9f8cd5ed-f5cf-4cf6-8c92-9fd0819238ca-5_675_1120_708_468}

1. Write down the coordinates of the points where the ellipse \(E\) intersects the coordinate axes.
2. The ellipse \(E\) is translated by the vector \(\left[ \begin{array} { c } p
   0 \end{array} \right]\), where \(p\) is a constant. Write down the equation of the translated ellipse.
3. Show that, if the translated ellipse intersects the line \(L\), the \(x\)-coordinates of the points of intersection must satisfy the equation $$9 x ^ { 2 } - ( 8 p - 40 ) x + \left( 4 p ^ { 2 } + 60 \right) = 0$$
4. Given that the line \(L\) is a tangent to the translated ellipse, find the coordinates of the two possible points of contact.
   (No credit will be given for solutions based on differentiation.)