2 weather-monitoring satellites orbit the earth.
One is in a circular orbit C₁, the other orbits in an extreme ellipse, C₂ so that it can get closer to the surface.
These orbits can be modelled by the equations below:
\[C_{1}:\left( x + 2\sqrt{17} \right)^{2} + y^{2} = 66\]
\[C_{2}:x = 10\cos t,\ y = 4\sqrt{2}\sin t,\ 0 \leq t \leq 2\pi\]
Give the x coordinate of the points of intersection of the curves C₁ and C₂, given that
\(- 5 \leq x \leq 0\). Give an exact answer in the form
\[A\sqrt{1122} + B\sqrt{17}\]
[7 marks]
