Match the following: Column - IColumn - II(i) If straight lines y = a1x + b and y = a2x + b meet the coordinate axes in con-cyclic points then[A] a1a2 > 0(ii) If the circles x2 + y2 + 2a1x + b = 0 touch each other then[B] b2 = a1a2(iii) If in (B) the first circle lies completely inside the second circle then[C] b > 0(iv) If the chord of contact of the tangents drawn to x2 + y2 = b2 from any point on x2 + y2 = a22 touches the circle x2 + y2 = a21, then (In all the cases a1 ≠ a2)[D] b = 0

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Maths Circle and System of Circles Mix Matrix Match Questions

Published on: August 14, 2026

Match the following:

Column - I	Column - II
(i) If straight lines y = a1x + b and y = a2x + b meet the coordinate axes in con-cyclic points then	[A] a1a2 > 0
(ii) If the circles x2 + y2 + 2a1x + b = 0 touch each other then	[B] b2 = a1a2
(iii) If in (B) the first circle lies completely inside the second circle then	[C] b > 0
(iv) If the chord of contact of the tangents drawn to x2 + y2 = b2 from any point on x2 + y2 = a22 touches the circle x2 + y2 = a21, then (In all the cases a1 ≠ a2)	[D] b = 0

Correct Matrix Matching

Verified by Experts

The correct answer is:

(i) [A]; (ii) [D]; (iii)[B]; (iv)[A]

Ans.

(i) [A][B][C]

(ii) [D]

(iii)[B]

(iv)[A][B][C]

Sol.

(i) a 1 a 2 > 0, b 2 = a 1 a 2 , b > 0

(ii) b = 0

(iii) b 2 = a 1 a 2

(iv) a 1 a 2 > 0, b 2 = a 1 a 2 , b > 0

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