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geom3d

 powerps
 compute power of a given point with respect to a given sphere

 Calling Sequence powerps(P, s)

Parameters

 P - point s - sphere

Description

 • The power of point P with respect to sphere s is $-{R}^{2}+{d}^{2}$ where d is the distance from point P to the center of s, and R is the radius of s.
 • The command with(geom3d,powerps) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$
 > $\mathrm{point}\left(o,X,Y,Z\right):$$\mathrm{assume}\left(0
 > $\mathrm{sphere}\left(s,\left[o,k\right]\right):$
 > $\mathrm{point}\left(P,\left[\mathrm{x1},\mathrm{y1},\mathrm{z1}\right]\right):$
 > $\mathrm{powerps}\left(P,s\right)$
 ${\left({X}{-}{\mathrm{x1}}\right)}^{{2}}{+}{\left({Y}{-}{\mathrm{y1}}\right)}^{{2}}{+}{\left({Z}{-}{\mathrm{z1}}\right)}^{{2}}{-}{{\mathrm{k~}}}^{{2}}$ (1)