find the radical plane of two given spheres - Maple Help

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geom3d[RadicalPlane] - find the radical plane of two given spheres

geom3d[RadicalLine] - find the radical line of three given spheres

geom3d[RadicalCenter] - find the radical center of four given spheres

Calling Sequence

RadicalPlane(p1, s1, s2)

RadicalLine(p1, s1, s2, s3)

RadicalCenter(p1, s1, s2, s3, s4)

Parameters

p

-

name

s1, s2, s3, s4

-

spheres

Description

• 

The locus of points Px,y,z which have the same power with respect to the two given spheres s1, s2 is a plane called radical plane.

• 

Let us introduce a third sphere s3. Now we have three radical planes that form a pencil whose axis is the straight line. This line is called the radical line of the three sphere.

• 

Now add a fourth sphere s4, and we have four radical lines. These four lines are clearly concurrent at the radical center.

Examples

withgeom3d:

Define two spheres s1, s2

spheres1,x2+y2+z2=1,x,y,z:

spheres2,pointB,5,5,5,2:

Find the radical plane of s1 and s2

RadicalPlanep,s1,s2

p

(1)

Equationp

72+10x+10y+10z=0

(2)

NormalVectorp

10,10,10

(3)

Simple check:

Generate a randpoint point on the radical plane:

randpointP,p

P

(4)

The power of point P with respect to two spheres s1 and s2 must be the same:

powerpsP,s1powerpsP,s2

0

(5)

Plotting:

drawp,s1,s2,style=patchnogrid,orientation=26,96,lightmodel=light1,title=`Radical plane of two given spheres`

Find the radical line of three spheres:

spheres3,pointA,1,2,3,3

s3

(6)

RadicalLinel,s1,s2,s3

l

(7)

detaill

Warning, assume that the parameter in the parametric equations is _t

name of the objectlform of the objectline3dequation of the linex=575+20_t,y=21540_t,z=20_t

(8)

Find the radical center of four given spheres:

spheres4,pointA,3,7,1,3

s4

(9)

RadicalCenterP,s1,s2,s3,s4

P

(10)

formP

point3d

(11)

coordinatesP

249100,471100,0

(12)

See Also

geom3d[sphere]


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