find the polar of a given point with respect to a given sphere
polar(p, A, s)
the name of the polar
The polar of a point A with respect to a sphere is defined to be the locus of all points conjugate to A.
For a detailed description of the polar of p, use the routine detail.
The command with(geom3d,polar) allows the use of the abbreviated form of this command.
Write down the equations of the polars of the points 1,2,−1, 3,5,−2 and 0,12,−12 with respect to the sphere x2+y2+z2−3⁢x+y+z−5=0 and show that they form a pencil of planes.
name of the objectp3form of the objectplane3dequation of the plane−5−3⁢x2+y=0
The answers show that three planes p1, p2, and p3 form a pencil of planes.
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