\(X\) is a fixed point \((3,0)\), \(Y\) is the point \((0,a)\). A line is drawn through \(Y\) and perpendicular to \(XY\), meeting the \(x\)-axis at \(Q\). On this line a point \(P\) is taken so that \(Y\) is the mid-point of \(QP\). Find the coordinates of \(P\).
There is a lot of information here given in a verbal form. It is always useful to sketch the situation to make sense of what is being asked.
Find the equation of the locus of \(P\) for varying values of \(a\).
How are the coordinates of \(P\) related to each other?