Match Column I with Column II. Column I: (A) Number of common tangents of x 2 + y 2 − 4 x − 6 y − 3 = 0 and x 2 + y 2 + 2 x + 2 y + 1 = 0 . (B) If the common chord of x 2 + y 2 − 4 x − 4 y = 0 and x 2

Question

Match Column I with Column II. Column I: (A) Number of common tangents of $x^{2} + y^{2} - 4 x - 6 y - 3 = 0$ and $x^{2} + y^{2} + 2 x + 2 y + 1 = 0$ . (B) If the common chord of $x^{2} + y^{2} - 4 x - 4 y = 0$ and $x^{2} + y^{2} = 16$ subtends an angle $π / k$ at the origin, find $k$ . (C) Shortest distance from $(2, - 7)$ to $x^{2} + y^{2} - 14 x - 10 y - 151 = 0$ . (D) Minimum of $x^{2} + y^{2}$ subject to $(x + 5)^{2} + (y - 12)^{2} = 1 4^{2}$ . Column II: (p) 2 (q) 0 (r) 3 (s) 1

Column I	Column II
(A) Number of common tangents of x²+y²-4x-6y-3=0 and x²+y²+2x+2y+1=0	(p) 2
(B) Common chord of x²+y²-4x-4y=0 and x²+y²=16 subtends angle π/k at origin; find k	(q) 0
(C) Shortest distance from (2,-7) to x²+y²-14x-10y-151=0	(r) 3
(D) Minimum of √(x²+y²), given (x+5)²+(y-12)²=14²	(s) 1

TestHub · Accepted Answer

A: radii 4,1 and centre distance 5 give three tangents. B: the common chord is x + y = 4 , at distance 2 2 ​ from the origin on the radius-4 circle, so its central angle is π /2 and k = 2 . C: centre ( 7 , 5 ) and radius 15; point-centre distance 13, so nearest distance 2. D: the circle has centre (-5, 12) at distance 13 from the origin and radius 14, so nearest distance 1.

Mathematics - Circle Question with Solution | TestHub

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