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geometry

 Polar
 find the polar of a given point with respect to a given conic or a given circle

 Calling Sequence Polar(l, P, c)

Parameters

 l - the name of the polar A - point e - conic or circle

Description

 • Let $c=\mathrm{O}\left(r\right)$ be a fixed circle, and let P be any ordinary point other than O. Let P' be the inverse of P in circle c. Then the line p through P' and perpendicular to OPP' is called the polar of P for the circle c. Since the package does not work with the extended plane, the routine does not find the polar of center O or of the ideal point.
 • If the point lies on the conic then the polar of P is the tangent line of the conic at that point.
 • For a detailed description of the polar of P, use the routine detail
 • The command with(geometry,Polar) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{circle}\left(c,{x}^{2}+{y}^{2}=1,\left[x,y\right]\right),\mathrm{ellipse}\left(e,\frac{{x}^{2}}{4}+{y}^{2}=1,\left[x,y\right]\right):$
 > $\mathrm{point}\left(A,3,0\right):$
 > $\mathrm{Polar}\left(\mathrm{l1},A,c\right)$
 ${\mathrm{l1}}$ (1)
 > $\mathrm{Equation}\left(\mathrm{l1}\right)$
 ${-}{1}{+}{3}{}{x}{=}{0}$ (2)
 > $\mathrm{Polar}\left(\mathrm{l2},A,e\right)$
 ${\mathrm{l2}}$ (3)
 > $\mathrm{detail}\left(\mathrm{l2}\right)$
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{l2}}\\ {\text{form of the object}}& {\mathrm{line2d}}\\ {\text{equation of the line}}& {-}{1}{+}\frac{{3}{}{x}}{{4}}{=}{0}\end{array}$ (4)

 See Also

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