91Ó°ÊÓ

Find the equation of the cylinder, whose guiding curve is \(x^{2}+z^{2}-4 x-2 z+4=0\), \(y=0\) and whose axis contains the point \((0,3,0)\). Find also the area of the section of the cylinder by a plane parallel to the \(x z\) plane.

A cylinder cuts the plane \(z=0\) with curve \(x^{2}+\frac{y^{2}}{4}=\frac{1}{4}\) and has its axis parallel to \(3 x=-6 y=2 z\). Find its equation.

Find the equation of the right circular cylinder of radius 2 whose axis passes through \((1,2,3)\) and has direction cosines proportional \(2,-3,6\).

Find the equation of the right circular cylinder of radius 1 with axis as \(\frac{x-1}{2}=\frac{y}{3}=\frac{z-3}{1}\)