Cylinder

• A cylinder is a surface generated by a moving straight line (generator) which is parallel to a fixed line and interescts a given surface or curve (guiding curve).

• The equation of the cylinder whose generators are parallel to the line ${\displaystyle \frac{x}{l}}={\displaystyle \frac{y}{m}}={\displaystyle \frac{z}{n}}$ and base conic is $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$, $z=0$ is given by:

$a(nx-lz{)}^2$+$2h(nx-lz)(ny-mz)$+$b(ny-mz{)}^2$+$2gn(nx-lz)$+$2fn(ny-mz)$+$c{n}^2=0$

• A right circular cylinder is a cylinder whose generator lines are at a constant distance (radius) from the fixed line (axis).

• The equation of the right circular cylinder with axis as the $z-axis$ and radius $a$ is given by $x^2+y^2=a^2$

• The equation of the right circular cylinder whose radius is $a$ and axis the line ${\displaystyle \frac{x-x_1}{l}}={\displaystyle \frac{y-y_1}{m}}={\displaystyle \frac{z-z_1}{n}}$ is given by:

${\displaystyle \frac{{[l(x-x_1)+m(y-y_1)+n(z-z_1)]}^2}{l^2+m^2+n^2}}$+$r^2$=${(x-x_1)}^2$+${(y-y_1)}^2$+${(z-z_1)}^2$

Cylinder