|
geom3d[polar] - find the polar of a given point with respect to a given sphere
|
|
Calling Sequence
|
|
polar(p, A, s)
|
|
|
Parameters
|
|
|
p
|
-
|
the name of the polar
|
|
A
|
-
|
point
|
|
s
|
-
|
sphere
|
|
|
|
|
|
Description
|
|
|
•
|
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.
|
|
|
|
Examples
|
|
|
>
|
|
Write down the equations of the polars of the points (1,2,-1), (3,5,-2) and (0,1/2,-1/2) with respect to the sphere x^2+y^2+z^2- 3*x+y+z-5=0 and show that they form a pencil of planes.
|
>
|
|
|
| (1) |
|
>
|
![sphere(s, x^2+y^2+z^2-3*x+y+z-5 = 0, [x, y, z])](/support/helpjp/helpview.aspx?si=5941/file04021/math92.png)
|
|
>
|
|
|
| (2) |
|
>
|
|
|
| (3) |
|
>
|
|
|
| (4) |
|
>
|
|
|
| (5) |
|
>
|
|
|
| (6) |
|
>
|
|
|
| (7) |
|
>
|
|
|
| (8) |
|
>
|
|
|
| (9) |
The answers show that three planes p1, p2, and p3 form a pencil of planes.
|
|
Download Help Document
Was this information helpful?
