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    Show that the envelope of the family of circles which pass through the origin and have centres on the curve  x^2+y^2-2x=0 is the cardioid with polar equation  r=2(1+\cos \theta ).
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    (Original post by Ano123)
    Show that the envelope of the family of circles which pass through the origin and have centres on the curve  x^2+y^2-2x=0 is the cardioid with polar equation  r=2(1+\cos \theta ).
    I asked this a few years ago, see how far you can get with the comments:
    http://www.thestudentroom.co.uk/show....php?t=2248274

    @ghostwalker - any progress on this question in the last three years?
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    (Original post by Blazy)
    @ghostwalker - any progress on this question in the last three years?
    Nope. Given my comment on that thread of the working being rather horrendous, I don't fancy looking at it again.
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    (Original post by Ano123)
    Show that the envelope of the family of circles which pass through the origin and have centres on the curve  x^2+y^2-2x=0 is the cardioid with polar equation  r=2(1+\cos \theta ).
    (Original post by ghostwalker)
    Nope. Given my comment on that thread of the working being rather horrendous, I don't fancy looking at it again.
    I gave it another shot. I think the parameterisation should've been  x = 1 + \cos(t) , which would lead to the right answer.
 
 
 
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