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📐 Mathematics  ·  Straight Lines  ·  JEE

The pair of lines 2x² + 5xy + 2y² = 0 represents:

Answer: Two parallel lines.

  • A Two parallel lines
  • B Two perpendicular lines
  • C Two lines at 45°
  • D Two coincident lines

Correct answer: A. Two parallel lines

Explanation: 2x² + 5xy + 2y² = (2x+y)(x+2y) = 0. The two lines: y = -2x and y = -x/2. Slopes -2 and -1/2, product = 1... not perpendicular. They are distinct lines.

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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