The line \(y = m x\) is a tangent to \(P _ { 2 }\)
Prove that \(m = \pm \sqrt { \frac { a } { b } }\)
Solutions using differentiation will be given no marks.
8
The line \(y = \sqrt { \frac { a } { b } } x\) meets \(P _ { 2 }\) at the point \(D\).
The finite region \(R\) is bounded by the \(x\)-axis, \(P _ { 2 }\) and a line through \(D\) perpendicular to the \(x\)-axis.
The region \(R\) is rotated through \(2 \pi\) radians about the \(x\)-axis to form a solid.
Find, in terms of \(a\) and \(b\), the volume of this solid.
Fully justify your answer.
Find the eigenvalues and corresponding eigenvectors of the matrix