9. A circle \(C\) has equation
$$( x - k ) ^ { 2 } + ( y - 2 k ) ^ { 2 } = k + 7$$
where \(k\) is a positive constant.
- Write down, in terms of \(k\),
- the coordinates of the centre of \(C\),
- the radius of \(C\).
Given that the point \(P ( 2,3 )\) lies on \(C\)
- show that \(5 k ^ { 2 } - 17 k + 6 = 0\)
- hence find the possible values of \(k\).
The tangent to the circle at \(P\) intersects the \(x\)-axis at point \(T\).
Given that \(k < 2\)
- calculate the exact area of triangle \(O P T\).