The Major Parts, Properties, And Uses Of A Hyperbola

In coordinate geometry, there are multiple figures that you can study. One of them is the hyperbola which consists of two equal curves. It lies as a mirror image to one another on the sides of the axis. These curves are infinite and do not have any end. You can take a common distance between the points of the curve. 

Hyperbola

Mathematicians term that portion as the focal point present in a hyperbola. It looks exactly like two circles that overlap each other in a plane. It can be defined with a standard equation in the graph which is, [(x2 / a2) – (y2 / b2)] = 1.


Context

  • Major Parts, Properties, And Uses Of A Hyperbola
      • Important regions in a hyperbola
      • Some major properties
      • Practical uses
  • Conclusion


Major Parts, Properties, And Uses Of A Hyperbola

Important regions in a hyperbola

  • There is a fixed line that always goes through the focus. You can call that part the transverse axis of the figure. It lies at 90 degrees to the directrix present in a hyperbola. 
  • The major axis has to meet somewhere in the structure. The point where it meets is termed as the vertices. You can see them marked as small points in the figure. 
  • The center usually lies at an equal distance from both vertices. From there you can calculate to check that the focal length is equal. 
  • Besides the transverse axis, it consists of another line that passes through it. This is known as the conjugate axis and it is perpendicular to the former line. 
  • Latus rectum is a special category of chord present in a hyperbola. Like others, it is also perpendicular to the transverse axis. In addition to that, it will always come through one of the foci in the diagram.

Some major properties

Hyperbola cannot have just one focal point in the diagram. This is why many kids miss out on the fact that it has two foci and not just one. The distance from the center to these foci will always be equal. It cannot change as it will defy the conditions of the hyperbola. Besides the conjugate axis, you can draw another line similar to it. This parallel line that connects two focal points is what people call the directrix. 

As you all know that the transverse axis cannot lie just at any angle it wants to. It needs to be fully perpendicular to the directrix present in the diagram. Otherwise, it won't be able to pass through the focus only. As a result, you will find that the focus always exists at the same level as the vertices. All of these rests on the transverse axis together giving a set of points. There may be sums where the question will be asked for the length of the latus rectum. 

In such cases just use the formula 2 b square/ a directly. In some of the cases, both the transverse and conjugate axis have similar lengths. People refer to this hyperbola as the rectangular hyperbola as well. 

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Practical uses

Hyperbola can be used to find the distance between two points or sites. This method is known as Trilateration and it is widely used to figure out the points. Even in nuclear power plants, these designs are used. This is because it forms a really strong structure along with the steel bars. 

The shadows that you see in the wall from a home lamp are a hyperbola. To see more examples you can throw a stone on the calm surface of the water. You will see multiple curves which may overlap together and form a hyperbola. 


Conclusion

Hyperbola can be a bit confusing if you don't know the properties well. The online math classes in Cuemath are the best solution to research this topic.

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