Apollonius Revisited Equidistance

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Equilocus of: A circle C and a point A (outside of C) is the single branch of thehyperbola with foci A and C and the constant difference of distances equal to the radiusof circle C.Note the hyperbola bends towards the point and away from the circle.Proof: We wish to locate all points P such that PB=PA. As PB=PC-CB we have:PA=PC-CB and thus CB=PC-PA.As CB is the radius of the circle C it is a constant thus we have PC-PA=constantsatisfying the definition of a hyperbola with A and C as foci.
Equilocus of: A circle C and a point A (in its interior) is an ellipse with foci A and C andconstant sum of distances the radius of circle C.Exercise: Study the diagrams below to explain why ellipse described is the equilocus ofthe given point and circle containing the point.
Page 1 and 2: Apollonius Revisited:EquidistanceA
Page 3 and 4: Introduction and Motivation:Apollon
Page 5 and 6: Distance between: A circle C and a
Page 7 and 8: (B) EQUIDISTANCEDefinition: A point
Page 9 and 10: Research: Construct and investigate
Page 11: Equilocus of:(a)Two intersecting li
Page 15 and 16: Equilocus of: Two external circles
Page 17 and 18: Equilocus of: Two circles D inside
Page 19 and 20: (D) Apollonius Tangency Problems: E
Page 21 and 22: LLLTask: Construct a circle tangent
Page 23 and 24: LLCTask: Construct a circle tangent
Page 25 and 26: CCLTask: Construct a circle tangent
Page 27 and 28: Challenge: Study special cases not
Page 29 and 30: (c) a point and a hyperbolaAdvanced
Page 31 and 32: - Construct the perpendicular bisec
Page 33 and 34: -Hide all but the Focus, the direct
Page 35 and 36: -Construct a segment between M and
Page 37 and 38: - This tool will be handy if, say,
Page 39 and 40: Note: The difference between the di
Page 41 and 42: -Create a movable free point M on t
Page 43 and 44: -Hide all but the loci and two poin
Page 45 and 46: -Construct E and F, the intersectio

Apollonius Revisited Equidistance

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