Pole - Maple Help

geometry

 Pole
 find the pole of a given line with respect to a given conic or a given circle

 Calling Sequence Pole(P, p, c)

Parameters

 P - the name of the pole of the line p - line c - conic or circle

Description

 • The pole of a line p with respect to a circle c, center O is the inverse of foot of perpendicular from O to p.  Alternatively, the point of intersection of the polars of any two points on p.
 • For a detailed description of the pole of P, use the routine detail.
 • The command with(geometry,Pole) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{_EnvHorizontalName}≔'x':$$\mathrm{_EnvVerticalName}≔'y':$
 > $\mathrm{circle}\left(c,{x}^{2}+{y}^{2}=1\right),\mathrm{ellipse}\left(e,\frac{{x}^{2}}{4}+{y}^{2}=1\right)$
 ${c}{,}{e}$ (1)
 > $\mathrm{line}\left(\mathrm{l1},3x-1=0\right),\mathrm{line}\left(\mathrm{l2},\frac{3}{4}x-1=0\right)$
 ${\mathrm{l1}}{,}{\mathrm{l2}}$ (2)
 > $\mathrm{Pole}\left(\mathrm{P1},\mathrm{l1},c\right)$
 ${\mathrm{P1}}$ (3)
 > $\mathrm{coordinates}\left(\mathrm{P1}\right)$
 $\left[{3}{,}{0}\right]$ (4)
 > $\mathrm{Pole}\left(\mathrm{P2},\mathrm{l2},e\right)$
 ${\mathrm{P2}}$ (5)
 > $\mathrm{coordinates}\left(\mathrm{P2}\right)$
 $\left[{3}{,}{0}\right]$ (6)