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 the 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 the directrix and axis.
6. Tangents drawn to any point on the directrix are perpendicular.
7. The rays incident parallel to the axis of symmetry get reflected off the surface and converge at the focus.
Examples of Parabola
1. Kicking the ball
When you kick a soccer ball, it arcs up into the air and comes down again, following the path of a parabola.
2. Shooting an arrow
When you shoot an arrow, it arcs up into the air and comes down again, following the path of a parabola.
3. Throwing a stone
When you throw a stone, it arcs up into the air and comes down again, following the path of a parabola.
4. Satellite Dishes
A satellite dish is a type of parabolic antenna that receives or transmits information by radio waves to or from a communication satellite.
5. Parabolic trough
Parabolic troughs are solar thermal collectors that are curved in three dimensions as a parabola, lined with polished metal mirrors. These are many used to concentrate the sun’s rays to make a hot spot.
6. Spotlight reflectors
Spotlights have parabolic reflectors that are used to project a bright beam of light onto a performance space.
7. Flashlight
A flashlight or torch has a parabolic reflector that gives a variable-focus effect from a wide floodlight to a narrow beam.
8. Parabolic microphone
A parabolic microphone has a parabolic reflector that collects and focuses sound waves onto a transducer.
9. Automobile headlight
Automobile headlamps have parabolic reflectors that collect and focus the beam of light to illuminate the road ahead.
10. Ballistic missile
A Ballistic missile delivers warheads on a target by using projectile motion. The trajectory of these missiles makes a parabolic path.
Parabolic path of a ballistic missile
11. Jump of a Dolphin
The jump of a dolphin is known as porpoising. According to some research, dolphins use their jump as a method of communication. If you look at a dolphin’s porpoising, you will observe that they trace a parabolic path while performing the jump.
12. Camera
Many cameras use an assembly of parabolic mirrors to take wide-angle shots.
13. IR Spectrometer
Some gated spectrometers use a pair of 90-degree off-axis parabolic mirrors to relay the light from an entrance slit to an output IR recording camera.
Optical components used for the IR spectrometer
14. Parabolic dunes
Parabolic dunes are formed when strong winds erode a section of the vegetated sand (commonly referred to as a blowout). Parabolic dunes are common in the sand sheet southwest of the main dune field.
15. Reflecting telescopes
Some reflecting telescopes use parabolic mirrors to reduce spherical aberration with no chromatic aberration.
A telescope with parabolic mirrors
16. Parabolic Wifi antenna
A parabolic wifi device uses a parabolic antenna that is backed with a parabolic reflector that directs waves, in this case, wifi waves, to the antenna, enhancing the wifi signal.
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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.