Wolfram Cloud Document

TwoPencilsApolloniusCircles::usage="The circles of Apollonius are formed by two pencils:The first is the ratio r of the distances from one point P to two fixed points C and D, denoted as follows: P{x, y} |

PC

PD

= r The second is the geometric locus of the P{x, y} that form an inscribed angle θ with the fixed points C and D, it is denoted as follows: P{x, y} | C



P

D = θ .References: Public domain; Personal adaptation. ";

Development:

Let the fixed points C{-5, 0} and D{5, 0}:

In[]:=

SwatchLegend[{Blue,Red},{"First pencil","Second pencil"}]ShowTableContourPlot

2

(x+5)

+

2

y

2

(x-5)

+

2

y

==r,{x,-10,10},{y,-10,10},ContourStyle{Blue,Thick},PerformanceGoal->"Quality",PlotPoints->60,r,0,5,

1

5

,TableContourPlotTan[θ]==

10y

2

x

+

2

y

-25

,{x,-10,10},{y,-10,10},ContourStyle{Red,Thick},PerformanceGoal->"Quality",PlotPoints->60,θ,0,π,

π

12

,Graphics[{Black,PointSize[0.01],Point[{-5,0}]}],Graphics[{Black,PointSize[0.01],Point[{5,0}]}],AxesTrue,ImageSize700,PlotRangeAll,AxesOrigin{0,0},AspectRatio->Automatic

Out[]=

	First pencil
	Second pencil

Out[]=