15.
Diagram not drawn to scale
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\includegraphics[alt={},max width=\textwidth]{4b084faa-a680-4f35-bb5c-a4edf5171b5f-22_725_844_251_623}
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\caption{Figure 3}
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The curve \(C _ { 1 }\), shown in Figure 3, has equation \(y = 4 x ^ { 2 } - 6 x + 4\).
The point \(P \left( \frac { 1 } { 2 } , 2 \right)\) lies on \(C _ { 1 }\)
The curve \(C _ { 2 }\), also shown in Figure 3, has equation \(y = \frac { 1 } { 2 } x + \ln ( 2 x )\).
The normal to \(C _ { 1 }\) at the point \(P\) meets \(C _ { 2 }\) at the point \(Q\).
Find the exact coordinates of \(Q\).
(Solutions based entirely on graphical or numerical methods are not acceptable.)