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📐 Mathematics  ·  Straight Lines  ·  JEE

The asymptotes of hyperbola x²/a² - y²/b² = 1 are:

Answer: y = ±(b/a)x.

  • A y = ±(a/b)x
  • B y = ±(b/a)x
  • C y = ±a
  • D y = ±b

Correct answer: B. y = ±(b/a)x

Explanation: Set y²/b² = x²/a² (hyperbola approaches these lines). Rearranging: y/b = ±x/a, so y = ±(b/a)x. These lines pass through the origin with slopes ±b/a. Ans: y = ±(b/a)x.

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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