10 The diagram below shows an ellipse \(E\)
The coordinate axes are the lines of symmetry of \(E\)
\includegraphics[max width=\textwidth, alt={}, center]{fd9715c4-9ce1-4608-aed6-f3d4f71208b5-14_645_780_450_630}
10
- Write down an equation of \(E\)
10
- The region bounded by the \(x\)-axis and the ellipse \(E\) for \(y \geq 0\) is shaded in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{fd9715c4-9ce1-4608-aed6-f3d4f71208b5-15_643_775_408_635}
A solid \(S\) is formed by rotating the shaded region through \(360 ^ { \circ }\) about the \(x\)-axis. Show that the volume of \(S\) is \(a \pi\) where \(a\) is an integer to be found.
\includegraphics[max width=\textwidth, alt={}, center]{fd9715c4-9ce1-4608-aed6-f3d4f71208b5-16_2488_1732_219_139}