A circular cylinder of volume \((3\sqrt5-4)\pi\) cm\(^3\) has a height of \((3+\sqrt5)\) cm and a radius of \(r\) cm. Obtain an expression of \(r^2\) in the form \(\dfrac{a+b\sqrt5}{c}\), where \(a\), \(b\) and \(c\) are constants.[4]
The line \(x-y=3\) intersects the curve \(x^2-3xy+y^2+19=0\) at points \(P\) and \(Q\). Find the coordinates of \(P\) and of \(Q\).[4]
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