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3 conic section types:  

Parabola (when a cone is cut in a direction parallel to the cone's slanted side)

Hyperbola (when a cone is cut at a vertical angle, perpendicular to the flat base)

Ellipse (when a cone is cut at any other angle than a parabola or hyperbola) - a circle is a special version of an ellipse, when a cone is cut parallel to the flat base side, at a right-angle to the hyperbola.


Parabola real-life examples/uses:  the shape through the air that a ball or other projectile travels; the shape of the top surface of liquid in a rotating container - visualize a jar of water on a spinning turntable; reflector in a flashlight, round radar or microwave antenna, or reflecting telescope - these all allow light or sound or radio waves to be either sent out in a straight line from a single point, or do the opposite: collect incoming light or energy into a single point.

Hyperbola real-life examples/uses:  we can predict the path a satellite will take when it passes near the moon or another planet - gravity bends the satellite path in a hyperbolic shape; the shape used for many microscope and similar lenses, to help our eyes focus correctly; the shape of many nuclear reactor cooling towers - the hyperbola allows using the least amount of easily-formed materials (like straight beams) to build a structure of the needed diameter and height ratio.

Ellipse (including the circle, for which you can find many examples in life) real-life examples/uses:  since an ellipse has two focii (plural of focus), rather than only one like a parabola, the ellipse makes a great whispering gallery, where one person can whisper at one focus, and someone at the other focus (which may be far away) can clearly hear it;  an ellipitical trainer, used to simulate running indoors, copies the ellipitical motion your foot normally makes when running; the shape many cooks cut foods into, to make them more attractive (like cucumbers, carrots, potatoes, and similar)