The graph \(y = x^2\) meets the line \(y = k\) (where \(k>0\)) at points \(P\) and \(Q\) as shown in the diagram. The length of the interval \(PQ\) is \(L\).
Let \(a\) be a positive number. The graph \(y=\dfrac{x^2}{a^2}\) meets the line \(y=k\) at points \(S\) and \(T\).
What is the length of \(ST\)?
- \(\dfrac{L}{a}\)
- \(\dfrac{L}{a^2}\)
- \(aL\)
- \(a^2L\)