A parabola is nothing but a U-shaped plane curve. Any point on the parabola is equidistant from a fixed point called the focus and a fixed straight line known as the directrix.
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Terms related to Parabola
1. Focus
Any point on the parabola is equidistant from a fixed point and a fixed straight line. Here, the fixed point is known as the focus. It lies on the axis of symmetry of the parabola.
2. Directrix
Any point on the parabola is equidistant from a fixed point and a fixed straight line. Here, the fixed straight line is known as the directrix. Directrix is perpendicular to the axis of symmetry of the parabola.
3. Axis of Symmetry
The axis of symmetry is an imaginary straight line that is perpendicular to the directrix and passes through the focus.
4. Vertex
Vertex is the point where the parabola makes its sharpest turn. It is located right in the middle of focus and the directrix.
Properties of Parabola
1. Eccentricity is the measure of the amount by which a figure deviates from a circle. The eccentricity of any parabola is 1.
2. Parabolas are symmetric about their axis.
3. The axis of symmetry passes through the vertex and the focus and is perpendicular to the directrix.
4. A tangent drawn at the vertex of a parabola is parallel to the directrix.
5. The vertex is the midpoint of the focus and the point of intersection of directrix and axis.
6. Tangents drawn to any point on the directrix are perpendicular.
7. The rays incident parallel to the axis of symmetry gets reflected off the surface and converge at the focus.
Examples of Parabola
1. Shape of a Banana
The curved shape of a banana closely resembles a parabola. Hence, it is one of the best examples of parabolic objects used in everyday life.
2. Roller Coasters
The curves of a roller coaster track can be easily observed and compared with the shape of a parabola. Hence, the ups and downs of a roller coaster are yet another example of parabola in real life.
3. Bridges
The bridges like tied-arch bridges, through arch bridges, cable-stayed bridges, etc., are u-shaped. Also, the supporting structure build under a bridge is curved or parabolic in nature.
4. Arch
An arch is a curved structure that provides strength to a building or a structure by compressing the stress downwards and outwards. It is also used to add an attractive look to the premises. An arch is curved in shape; therefore, it is a classic example of a parabola in real life.
5. Slinky Toy
When a slinky toy is stretched and placed on the top of a rigid surface in such a way that both of its ends properly touch the base of the surface, one can easily observe the parabolic shape formed by it.
6. Brand Name Logos
Some of the brands incorporate the parabolic shape in designing their logos. For instance, if you notice the logo of the food brand McDonald’s, it consists of a curved ‘M’ alphabet. The curves of the letter ‘M’ display a perfect example of a parabola in real life.
7. Rainbow
A rainbow is a U-shaped seven coloured curve that appears in the sky after or during the rain. Hence, it is yet another example of a parabolic shape in nature.
8. Wheel Pose
While doing yoga you must have practised the wheel pose or the chakra-asana. While practising the wheel pose, the shape of the human body appears to be an inverted U alphabet. Hence, it is one of the best examples of parabola in real life.
9. Parabolic Dish Antennas
As the name suggests, parabolic dish antennas are constructed in the shape of the parabolic geometric figure. The purpose is to exchange signals between the source and the destination. The main advantage of utilizing the parabola concept in designing an antenna is that the directivity improves significantly.
10. Swing Belt
The belt of a swing is usually parabolic in shape, except for certain designs where the seat attached to the play swing is a flat board.
11. Jump of a Dolphin
The jump of a dolphin is known as porpoising. A number of researches show that dolphins use their jump as a method of communication. If you look at a dolphin porpoising, you will observe that they trace a parabolic path while performing the jump. Hence, it is yet another example of parabolic shape in real life.
12. Projectile Motion of Objects
When an object exhibits motion in both vertical and horizontal direction at the same time, it is said to be exhibiting a projectile motion. If you trace the path followed by an object while exhibiting projectile motion, you can easily plot a parabolic curve. Hence, the projectile motion of objects is one of the perfect examples of parabola in real life.
13. Chain tied to Poles on Sidewalk
The chain tied to the poles present on the sidewalk hangs vaguely in the centre and is stretched on the edges. If you observe the shape formed by such chains, you can very easily identify the parabolic figure.
14. Water coming out of Fountains
Most of the fountains make use of the laminar flow of water for decorative purposes. The water coming out of such fountains display a parabolic shape in real life. A similar parabolic shape can be seen by looking at the water coming out of a drinking fountain.
15. Top of a Bread Loaf
A bread loaf is curved on the top. Hence, the parabolic shape can be observed easily.
16. Sparkles of Fire Crackers
When a firecracker is launched into the air, it explodes after reaching a certain height. The chemical substance contained by the firecracker then releases colourful sparkles in the sky. These sparkles usually tend to form a parabolic shape that can be easily observed by an observer standing on the earth.
It is very parctical exaples you presented. and helpful to develop better undersatandin of Parabola in real life.
Suspension bridges, hanging chains, high tension cables, all have the same shape: catenary.