Find the coordinates of the midpoint of \(A B\).
6
Show that the equation of the circle may be written as
$$x ^ { 2 } + y ^ { 2 } - 8 x - 2 y = 1$$
6
\(\quad\) The circle has centre \(C\) and crosses the \(x\)-axis at points \(D\) and \(E\). Find the exact area of triangle \(D E C\).
6
The circle has centre \(C\) and crosses the \(x\)-axis at points \(D\) and \(E\).
The area enclosed between the curve and the \(x\)-axis is 36 units.
Find the value of \(a\).
Fully justify your answer. [0pt]
[6 marks]
\(7 \quad\) A curve has equation \(y = a ^ { 2 } - x ^ { 2 }\), where \(a > 0\)