36) If the radius of the circumcircle of the triangle TPQ, where PQ is chord of contact corresponding to point t with respect to circle x 2 + y 2 - 2 x + 4 y - 11 = 0 , is 12 units, then minimum distance of t from the director circle of the given circles is .

a )   6 b )   12 c )   6 2 d )   24 - 4 2

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Please find below the solution to the asked query:

x2+y2-2x-4y-11=0x2-2x+y2-4y-11=0x-12-1+y-22-4-11=0x-12+y-22=16=42Hence equation of director cirlce will bex-12+y-22=422If Ois the centre of given circle, then we know thatT,P,Q,O are concyclic.


The shaded circle is director circle.NowAs TPO=90° As TP is tangentHence TO is diameter As Angle in semi circle is 90°TO=2×Radius=2×12=24 RO=Radius of director circle=42Minimum distance is obtained when T,R,O are along straight line.Min distance=TO-RO=24-42 Answer

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