7. The parabola \(C\) has equation \(y ^ { 2 } = 4 a x\), where \(a\) is a positive constant.
The line \(l\) with equation \(3 x - 4 y + 48 = 0\) is a tangent to \(C\) at the point \(P\).
- Show that \(a = 9\)
- Hence determine the coordinates of \(P\).
Given that the point \(S\) is the focus of \(C\) and that the line \(l\) crosses the directrix of \(C\) at the point \(A\),
- determine the exact area of triangle \(P S A\).
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| VIXV SIHIANI III IM IONOO | VIAV SIHI NI JYHAM ION OO | VI4V SIHI NI JLIYM ION OO |