The polar line of a point with respect to a conic.

The polar point of a line with respect to a conic.

A perfectly positive linear relationship would look something like this, but this and this are also positive relationships, whereas a negative linear relationship would look like this, but this and this are also negative relationships.

Construct a polar line wrt. this conic

Turn to the left without regard to the signal.

The answer is yes clearly for different values of A, I get different values of B.

curve

Curve

Curved

What about the second assumption?

A nice visual composition of symmetry.

Evolute of a curve

Splines

Spookiness

Hyperbola

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Bezier Curve

That's a p.

In particular, it could invent things like a curve which fills the plane.

Construct a polar point wrt. this conic

Directrix of a Conic

The directrix line of a conic.

Asymptotes of a Hyperbola

Tangent to This Curve

But there's a fair bit of variation around it, so I would say that the relationship is linear but not exact.

So as you see here, if I charge 2.80 and I only sell 300,000, then this is my return on asset right here.

And always keep in mind, the difference between demand which is this entire relationship, the entire curve, that we can move along if we hold everything else equal and only change price, and quantity demanded, which is a particular quantity for a particular price holding everything else equal.

C Curve

Conics

conic

cubic curve

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Hyperbola

But a hyperbola would look something like this. They get to be right here and they get really close to the asymptote.

Evolute of this curve

The line tangent to a curve

That an ellipse is just a squished circle.

Center of Curvature of This Curve

Let's say it moves in a path that moves something like this.

Bézier Curves

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Bézier Curve

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