What is a parabola?

How does a parabolic reflector improve the surface of a parabola?

  • The chord of the parabola that is parallel to the directrix and passes through the focus is known as the latus rectum. Parabolas can open in any direction: up, down, left, right, or any other. Here, \\ (a > 0\\), the parabola is opened up on the right side. If \\ (a < 0\\), the parabola will be opened up on the left side.

  • For example, a parabolic reflector helps in focusing light into a beam that can be seen from a long distance. It aids in the reduction of light utilisation, and so improves the surface of the parabola. Q.1. What will be the coordinates of focus and vertex for the parabola \\ ( {y^2} = 12x\\) ?

  • The parabola is U-shaped (opening to the top). The horizontal chord through the focus (see picture in opening section) is called the latus rectum; one half of it is the semi-latus rectum. The latus rectum is parallel to the directrix. The semi-latus rectum is designated by the letter p {displaystyle p} .

image-What is a parabola?
image-What is a parabola?
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