Parabolas are special

At the bakery, Simon tells me: “Parabola is the only shape that’s both an ellipse and a hyperbola (at least in a projective plane, which means that you can have a point at infinity). There are three ways to draw a parabola:

1. Graph y =x^2

2. Slice a cone parallel to its slope.

3. (Which we don’t really care about) Throw something.”

We buy modeling clay on the way home. He tries to reconstruct what he said about a parabola as a cross section of a cone.

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