And actually, just so you know, this equation right here, this is a particular hyperbola that opens to the left and the right.

And the way we show demand increasing is the whole curve shifts to the right so this right over here demand increased demand went up when income went up.

A point on the solution curve

And this is the case for most goods we call things like this, when income goes up, demand goes up, whole curve shifts to the right income goes down, demand goes down, whole curve shifts to the left

Select a point on the curve...

The slope is now downwards sloping.

You'll get the area of this rectangle, which might be a pretty good approximation for the area under the curve.

So your distance between the two left and right points in a horizontal ellipse is the same as the distance between the two

Start transport from this point of the curve

So the curve is the upper bound when we go upwards.

Turn to the right.

You go 1 2 3 minus 3, minus 1.

Take a right on Morrison Avenue.

Frito, take a right here. Right, right!

Turn right.

This is the asymptote.

And you'll get no solution.

Evolute of a curve

Turn right at the next corner.

Tangent to This Curve

Right?

It's either going to look like that, where it opens up to the right and left.

Let's see if we can learn a thing or two about the hyperbola.

So this is d1, and this is d2, so you have a situation and we could take the absolute value of the difference, because they might be, they might at some points d1 will be longer than d2 if you're on this curve.

Turn at the first corner to the right.

The best way to go right and then into the left lane is to take the right turn and then initiate a lane shift, which is happening right now, to reach a target location that is indicated by this big orange circle that it's crossing right now.

Take the first street to the right.

Check whether this point is on a curve

Check whether the point is on this curve

Directrix of a Conic

The directrix line of a conic.

Asymptotes of a Hyperbola

Turn right.

Louie?

Intersect this Conic

Intersect this Cubic Curve

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.

curve

Curve

Curved

Or the other way to think about it is, when you take the positive square root, when you take the positive square root, you're always going to be a little bit above the asymptote.

Turn right there.

Evolute of this curve

A nice visual composition of symmetry.

Transpose of a matrix is this original matrix with it's rows and columns flipped along the diagonal.