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The diagram shows the circle with equation \(x ^ { 2 } + y ^ { 2 } - 6 x + 4 y - 27 = 0\) and the tangent to the circle at the point \(P ( 5,4 )\).
- The tangent to the circle at \(P\) meets the \(x\)-axis at \(A\) and the \(y\)-axis at \(B\).
Find the area of triangle \(O A B\), where \(O\) is the origin.
- Points \(Q\) and \(R\) also lie on the circle, such that \(P Q R\) is an equilateral triangle.
Find the exact area of triangle \(P Q R\).
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.