Apollonius Revisited Equidistance

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Equilocus of: A line k and a circle C is a parabola with C the center of circle as its focusand a line k' shifted parallel to the given line k by the radius of the circle away from thecircle as its directrix.Exercise: Study the diagram below to explain why parabola described is the equilocus ofthe given line and circle.
Equilocus of: Two external circles C, D is a single branch hyperbola with the centers ofthe two circles C and D as its foci and the difference in the radii of circles (R-r) as theconstant difference in distances.Exercise: Study the diagrams below to explain why hyperbola described is the equilocusof the two given circles.
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 and 12: Equilocus of:(a)Two intersecting li
Page 13: Equilocus of: A circle C and a poin
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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