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📐 Mathematics  ·  Straight Lines  ·  JEE

The locus of midpoints of parallel chords of a parabola is:

Answer: A diameter (a line parallel to axis).

  • A Another parabola congruent to the original one
  • B A diameter (a line parallel to axis)
  • C A circle centred at the parabola's focus
  • D The axis of the parabola itself, exactly

Correct answer: B. A diameter (a line parallel to axis)

Explanation: The locus of midpoints of parallel chords of a parabola is a line parallel to the axis of the parabola (a diameter of the parabola).

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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