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📐 Mathematics  ·  Straight Lines  ·  JEE

Three circles pass through the origin. The radical axis of any two of them:

Answer: Is perpendicular to line joining centres.

  • A Passes through the origin in every possible configuration
  • B Is perpendicular to line joining centres
  • C Is parallel to the x-axis regardless of where the centres lie
  • D Cannot be determined without knowing the radii of all three circles

Correct answer: B. Is perpendicular to line joining centres

Explanation: The radical axis of two circles is always perpendicular to the line joining their centres. This is a fundamental property.

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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