14. The circle \(C\) has equation
$$x ^ { 2 } + y ^ { 2 } + 16 y + k = 0$$
where \(k\) is a constant.
- Find the coordinates of the centre of \(C\).
Given that the radius of \(C\) is 10
- find the value of \(k\).
The point \(A ( a , - 16 )\), where \(a > 0\), lies on the circle \(C\). The tangent to \(C\) at the point \(A\) crosses the \(x\)-axis at the point \(D\) and crosses the \(y\)-axis at the point \(E\).
- Find the exact area of triangle \(O D E\).