Polar Line of a Point

Intersection of lines

Dot

The Dotted Line

Dots

Polar Point of a Line

On the left hand panel, again, we have the S shaped curve of adoption.

Points and lines

A point on the solution curve

Conic by Directrix, Focus Point

Dash Dot

Dash Dot Dot

What's the connection?

Inversion of Point, Line or Circle

Do you see?

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

Intersect with this line

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

So let's add a straight edge here, so this is to draw a line.

Let's call this line right over here line AB.

Select a point on the curve...

Hyperbola by Focuses Point

The midpoint of a segment or two other points

So that means that we're including the line.

And now we should be able to use this information to figure out the actual coordinates of the focus and the directrix of what I would call the classic parabola, y is equal to x squared.

Construct the polar line of this point

Check collinearity of this point

This is what it looks like.

Hyperbola by Asymptotes Point

Parabola by Directrix Focus

So that's what this equation will look like.

Tangent at This Point

So all of these scores are made up of weather data.

So if this is 1, 2, 3, 1, 2.

Construct the midpoint of this segment

Start transport from this point of the line

Start transport from this point of the curve

Intersect with this conic

Intersect with this cubic

Construct the polar point of this line

Intersect with this cubic curve

It looks like a parabola.

A half line by its start point, and another point somewhere on it.

Line by Two Points

So the line y equals x looks like that.