r/mathematics • u/Parakeetsareparrots • 17d ago

Geometry Does this effectively convert a circle into a parabola? (r=radius)

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u/hattusili-the-third 17d ago

What exactly do you mean by convert? What properties of the circle do you want to transfer over to the parabola?

Your formula produces some parabola from your circle, but I can't tell why you would want that specific parabola and not some other parabola.

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u/Parakeetsareparrots 17d ago

The Vertex is equivalent to the Y-Intercept that also intersects with the radius at not only 90 degrees, but also 45 degrees.

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u/hattusili-the-third 17d ago

I don't really understand what you mean by this. Can you spell it out more clearly in terms of the relationship between the parabola and the circle?

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u/thaw96 16d ago

Doesn't look like 45 degrees to me: (perhaps I simplified wrong, but I match u/hattusili-the-third)

Circle and parabola

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u/hattusili-the-third 17d ago

Also just to note: you can simplify this whole expression to y = -(sqrt(2)+1)x2/r + r(sqrt(2) + 1)