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📐 Mathematics  ·  Straight Lines  ·  JEE

Equation of normal to parabola y² = 4ax at point (at², 2at) is:

Answer: y = -tx + 2at + at³.

  • A y = -tx + 2at + at³
  • B y = tx - 2at - at³
  • C y = tx + 2at
  • D y = -tx + 2at

Correct answer: A. y = -tx + 2at + at³

Explanation: Slope of tangent at t is 1/t, so normal slope = −t. Normal through (at²,2at): y−2at=−t(x−at²), giving y=−tx+2at+at³. Verified: this is the standard normal form. Ans: y=−tx+2at+at³.

Slope as Rise over Runxy(x₁,y₁)(x₂,y₂)run = x₂−x₁rise = y₂−y₁m = rise/run = (y₂−y₁)/(x₂−x₁) = tanθ

The slope of a line is the ratio of vertical change (rise) to horizontal change (run) between any two points on it - equivalently, the tangent of the angle θ the line makes with the positive x-axis.

Concept context

Points, lines, and curves on the Cartesian plane

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