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JEE Main 2023
Conic Sections
Parabola
Easy

Question

If the xx-intercept of a focal chord of the parabola y2=8x+4y+4y^{2}=8x+4y+4 is 3, then the length of this chord is equal to ____________.

Answer: 2

Solution

This solution will guide you through finding the length of a focal chord of a parabola. We'll break down the problem into clear, manageable steps, explaining the mathematical reasoning behind each action.

Key Concepts and Formulas:

  1. Standard Form of a Parabola: For a parabola with its axis parallel to the x-axis, the standard form is (yk)2=4a(xh)(y-k)^2 = 4a(x-h), where (h,k)(h,k) is the vertex and aa is the focal length. The focus of such a parabola is located at (h+a,k)(h+a, k).
  2. Focal Chord: A chord of a parabola that passes through its focus.
  3. Length of a Focal Chord: For a parabola

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