APPLICATION OF CONIC SECTION, CITING EXAMPLE OF EACH

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)

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