Find the exact distance between the two points where the curve \(9(x-1)^2+4(y-3)^2=36\) cuts the \(y\)-axis.[4]
Find the coordinates of the points where the curve with equation \(2x^2+83xy=x^3y-20x\) intersects the curve with equation \(y=\dfrac1x\). 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.[6]
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