DO NOT USE A CALCULATOR IN THIS QUESTION. (a) Find the exact distance between the two points where the curve \(9(x-1)^{2}+4(y-3)^{2}=36\) cuts the \(y\)-axis. (b) Find the coordinates of the points where the curve with equation \(2 x^{2}+83 x y=x^{3} y-20 x\) intersects the curve with equation \(y=\frac{1}{x}\). Give each of your answers in the form \(a+b \sqrt{c}\), where \(a\) and \(b\) are rational and \(c\) is the smallest integer possible.