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Question 320008
JEE Mathematics · Hard

Circle: Two circles MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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Two circlesHardQuestion 320008

Question

Two circles are orthogonal if:
  1. A
    2g₁g₂ + 2f₁f₂ = c₁ + c₂
    Correct
  2. B
    Their centres coincide
  3. C
    They are concentric
  4. D
    r₁ = r₂

Correct answer

2g₁g₂ + 2f₁f₂ = c₁ + c₂

Explanation

Two circles are orthogonal (intersect at right angles) when 2g₁g₂ + 2f₁f₂ = c₁ + c₂. This ensures the tangent from one centre to the other circle passes through the intersection point at 90°.

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