Say you are walking along a parabola-shaped path, when you see a bear at the focus.

• Definition of a Parabola.
• Word Problems Using Parabolas - Expii.
• Writing Equations of Parabolas.
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If all other bears are on the other side of the directrix, then you are safe. But if there is a second bear on this side of the directrix, then watch out, because then your path will sometimes be nearer one bear and sometimes nearer the other, and when you get near this territorial boundary the bears will charge towards you to maintain their claim to you as food.

Real-life Examples of a Parabola for a Better Understanding

If you want to simulate a "point" reflector, that reflects waves aimed at the point directly back to their source, then might think you could use a mirrored ball centered at the point. But this has the problem that the waves arrive back at the source before they should.

To solve this, you can instead use the outside of a parabola together with a mirror on the directrix. Say there is a parabola-shaped lake, and you want to build two perpendicular roads, neither of which is blocked by the lake.

Finding the Maximum and Minimum

Where can the crossroads be? Answer: Anywhere on the far side of the directrix.

By the way, the two applications you mention for the focus are actually the same, since satellites are so far away that their faint signal needs to be collected in the same way as a whisper. This might not be what you're looking for, but here is a problem I've seen in a Calculus class. It doesn't really have a real-world application that I know of , but the directrix does come up in an interesting way. If you throw a ball, then ignoring air resistance it will have a parabolic trajectory.

Go Figure!: Parabola - The Arch Enemy?

The directrix of this parabola is a horizontal line, the set of all points at a certain height in the parabola's plane. This height is the energy in the ball. In other words, the potential energy that the ball would have if it were at rest at that height equals the potential plus kinetic energy of the ball everywhere on its parabolic path.

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So if the ball has elastic collisions with fixed objects walls, tables, or even oddly shaped objects , it will have a different parabolic trajectory after each bounce, but the directrix will always be at the same height as before. In fact, the common height of these directrices is the maximum height that the ball can reach.

If the ball was dropped from a certain height, then you can figure out what that height was, even several bounces later: it is always the height of the directrix of its current parabolic trajectory. Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site the association bonus does not count. Would you like to answer one of these unanswered questions instead? Home Questions Tags Users Unanswered. Real Life Examples.

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Reflective Properties. Results and Conclusions. The most common example is when you stir up orange juice in a glass by rotating it round its axis. The juice level rises round the edges while falling slightly in the center of the glass the axis. Another example of rotating liquids is the whirlpool. Parabolas are also used in satellite dishes to help reflect signals that then go to a receiver. This specific satellite is the National Radio Astronomy Observatory, which operates the world premiere astronomical telescope operating from centimeter to millimeter wavelengths, and is located in Green Bank, West Virginia.

Signals that go directly to the satellite will reflect off and back to the receiver after bouncing off the focus due to parabolas reflective properties. The cables that act as suspension on the Golden Gate Bridge are parabolas.