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📐 Mathematics  ·  Straight Lines  ·  JEE

The angle between two circles intersecting orthogonally satisfies:

Answer: Both A and B.

  • A 2g₁g₂ + 2f₁f₂ = c₁ + c₂
  • B The angle = 90°
  • C Both A and B
  • D Neither A nor B

Correct answer: C. Both A and B

Explanation: Orthogonal intersection means tangents at the meeting point are perpendicular (angle=90°). Using r₁²+r₂²=d² (sum of squared radii = squared distance between centres), this reduces to 2g₁g₂+2f₁f₂=c₁+c₂. Both statements are equivalent. Ans: Both A and B.

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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