Length of Tangent, Subtangnet, Normal and Sub-Normal :
Let the parabola is `y^2 = 4ax` . Let the tangent at any point `P(x, y)` meet the axis of parabola at `T` and `G` respectively and tangent makes an angle `psi ` with `x`-axis.
` :. tan psi =((dy)/(dx))_(P(x,y))` and `PN=y`
`:. PT =` length of tangent `= PN co se c psi= y c ose c psi`
`PG =` length of normal `= y sec psi`
`TN =` length of sub-tangent `= PN cot psi = y cot psi`
`NG =` length of sub-normal `= y tan psi`
` :. tan psi =((dy)/(dx))_(P(x,y))` and `PN=y`
`:. PT =` length of tangent `= PN co se c psi= y c ose c psi`
`PG =` length of normal `= y sec psi`
`TN =` length of sub-tangent `= PN cot psi = y cot psi`
`NG =` length of sub-normal `= y tan psi`