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Important Parabola Formulas For JEE

Important Parabola Formulas For JEE

by PW Gulf
September 19, 2023
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The Joint Entrance Examination (JEE) is one of the most competitive exams in India for admission to prestigious engineering institutes. In the mathematics section of JEE, topics like conic sections hold significant weightage. One of the fundamental conic sections is the parabola. In this article, we will explore important parabola formulas that are crucial for JEE preparation, helping you ace this challenging exam.

Standard Form of a Parabola:

The standard form of a parabola is given by the equation:
y = ax^2 + bx + c

  • "a" determines the direction and width of the parabola.
  • "a" is positive for a "U"-shaped parabola (opening upward) and negative for an inverted "U" shape (opening downward).
  • The vertex of the parabola is at (-b/2a, c - b^2/4a).

Vertex Form of a Parabola:

The vertex form of a parabola is given by the equation:
y = a(x - h)^2 + k

  • (h, k) represents the vertex of the parabola.
  • "a" determines the direction and width of the parabola as mentioned earlier.
  • For a "U"-shaped parabola, "a" is positive, and for an inverted "U" shape, "a" is negative.

Focus and Directrix:

  • For a parabola with a focus at point (p, 0):
    Vertex (0, 0), Focus (p, 0), and Directrix x = -p
  • For a parabola with a focus at point (0, p):
    Vertex (0, 0), Focus (0, p), and Directrix y = -p
  • The distance between the vertex and the focus (or vertex and directrix) is "p," called the focal length.

Axis of Symmetry:

  • The axis of symmetry for a parabola of the form y = ax^2 is the vertical line x = 0.

Latus Rectum:

  • The latus rectum is a line segment that passes through the focus and is perpendicular to the axis of symmetry. Its length is 4|a|.

Tangent to a Parabola:

  • The equation of the tangent line to a parabola at a point (x₁, y₁) is given by:
    y - y₁ = 2a(x - x₁)

Length of the Chord Parallel to the Axis:

  • If a chord parallel to the axis of symmetry intersects the parabola at two points with x-coordinates x₁ and x₂, then its length is given by:
    Length = |x₁ - x₂|

Parametric Equations:

Parametric equations for a parabola with its focus at the origin and the directrix along the y-axis are:
x = 2pt

  • y = pt^2
  • Here, "p" is the focal length, and "t" is a parameter.

Understanding parabola formulas is crucial for scoring well in the mathematics section of the JEE. These formulas allow you to analyze and solve problems related to parabolas efficiently. By mastering these concepts, you'll be well-equipped to tackle parabola-related questions and increase your chances of success in the JEE exam. Remember to practice and apply these formulas to various problem-solving scenarios to strengthen your skills further.

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