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Conic Sections

Conic Section: a section (or slice) through a cone.

Did you know that by taking different slices through a cone you can create a circle, an ellipse, a parabola or a hyperbola?

cones conic section circle conic section ellipse conic section parabola conic section hyperbola
Cones Circle Ellipse Parabola Hyperbola
  straight through slight angle parallel to edge of cone steep angle

So all those curves are related!


General Equation

In fact, we can make an equation that covers all these curves.

Because they are plane curves (even though cut out of the solid) we only have to deal with Cartesian ("x" and "y") Coordinates.

But these are not just straight lines, so just "x" and "y" will not do ... we need to go to the next level, and have x2 and y2, and also x (without y), y (without x), x and y together (xy) and a constant term.

We also need factors (A,B,C etc) so the general equation that covers all conic sections is:

Ax^2 etc

And from that equation we can create equations for the circle, ellipse, parabola and hyperbola ... but that is beyond the scope of this page.

Latus Rectum

latus rectum

No, it is not a rude word. It means the chord parallel to the directrix and passing through the focus.

It applies to all conic sections.

In a parabola, the length of the latus rectum is equal to four times the focal length.



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