The circle x² + y² = 4 cuts the circle x² + y² + 2x + 3y − …

Maths Circle and System of Circles General Single Correct MCQ

Published on: August 13, 2026

The circle x² + y² = 4 cuts the circle x² + y² + 2x + 3y − 5 = 0 in A & B. Then the equation of the circle on AB as a diameter is:

13(x² + y²) − 4x − 6y − 50 = 0

9(x² + y²) + 8x − 4y + 25 = 0

x² + y² − 5x + 2y + 72 = 0

13(x² + y²) − 4x − 6y + 50 = 0

Text Solution

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The correct answer is:

Common chord of given circle

2x + 3y – 1 = 0

family of circle passing through point of intersection of given circle

centre

This centre lies on AB

2 + 3 – 1 = 0 ⇒ –4 – 9 – 2 λ – 2 = 0 ⇒ 2 λ = –15 ⇒ λ = –15/2

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