Geometry

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 )

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/showthread.php?t=2248274

@ghostwalker - any progress on this question in the last three years?

(edited 7 years ago)

@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.

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.

Clearing 2024: how to call universities

What is an LLM and how could it benefit your career?

Powerful questions business students forget to ask their career advisers

Why I chose a law degree and what studying law was like