8 The curves \(\mathrm { y } = \mathrm { h } ( \mathrm { x } )\) and \(\mathrm { y } = \mathrm { h } ^ { - 1 } ( \mathrm { x } )\), where \(\mathrm { h } ( x ) = x ^ { 3 } - 8\), are shown below.
The curve \(\mathrm { y } = \mathrm { h } ( \mathrm { x } )\) crosses the \(x\)-axis at B and the \(y\)-axis at A.
The curve \(\mathrm { y } = \mathrm { h } ^ { - 1 } ( \mathrm { x } )\) crosses the \(x\)-axis at D and the \(y\)-axis at C .
\includegraphics[max width=\textwidth, alt={}, center]{c30a926b-d832-46f5-aa65-0066ef482c3d-7_826_819_520_255}

1. Find an expression for \(\mathrm { h } ^ { - 1 } ( x )\).
2. Determine the coordinates of A, B, C and D.
3. Determine the equation of the perpendicular bisector of AB . Give your answer in the form \(\mathrm { y } = \mathrm { mx } + c\), where \(m\) and \(c\) are constants to be determined.
4. Points A , B , C and D lie on a circle. Determine the equation of the circle. Give your answer in the form \(( x - a ) ^ { 2 } + ( y - b ) ^ { 2 } = r ^ { 2 }\), where \(a\), \(b\) and \(r ^ { 2 }\) are constants to be determined.