Apollonius Revisited Equidistance

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Research: Going beyond Apollonius: the strange new world of EquilociDefine distance between and then construct equilocus between(a) a point and a parabola(b) a point and an ellipse
(c) a point and a hyperbolaAdvanced Research: Really going beyond ApolloniusLet the notation representP:point, L:line, C:circle, R:parabola, E:ellipse, H:hyperbola(a)Construct the equilocus between any two conic sectionsRR, EE, HH, RE, RH, EH, CR, CE, CH etc.(b)Then explore how to construct a circle tangent to the given objects under allimaginable cases beyond the 10 basic ones considered by Apollonius:RRR, EEE, HHH, PPR, PPE, PPH, PRR, PEE, PHH, PRE, PRH, REH, etc. etc..
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 and 14: Equilocus of: A circle C and a poin
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: Challenge: Study special cases not
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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