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Q.

Consider the circle x2+y2+2x+4y20=0andx2+y2+6x8y+10=0 Then which of the following is (are) true

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a

Length of their common chord is 53/2

b

The circles are orthogonal 

c

Length of their common tangent is 5(125)1/4

d

The number of common tangents of circles is 2

answer is A, B, C, D.

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Detailed Solution

C1=(1,2),r1=5. C2=(3,4),r2=15. d=40   
r1+r2>d>r1r2 Hence circles intersect at two district point then there are two common tangents exist
2gg'+2ff'=10,C+C'=10 Orthogonal
Length of common tangent =d2(r1r2)2=5(125)1/4 
Length of common chord =2r1r2r12+r22=532

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