9709 P32 - Jun 2013 - Q5
1659
The diagram shows the curve with equation
\(x^3 + xy^2 + ay^2 - 3ax^2 = 0\),
where \(a\) is a positive constant. The maximum point on the curve is \(M\). Find the \(x\)-coordinate of \(M\) in terms of \(a\).
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