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Question

The angle between the circles S1:x2+y24x+6y+11=0 and S2:x2+y22x+8y+13=0 is

A
90o
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B
60o
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C
45o
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D
30o
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Solution

The correct option is C 45o
S1:x2+y24x+6y+11=0
C1(2,3), r1=2
S2:x2+y22x+8y+13=0
C2(1,4), r2=2

Distance between centres
d=|C1C2|
d=(21)2+(3+4)2=2

If angle between the circles is θ, then
cosθ=(r21+r22d22r1r2)
cosθ=(2+422×2×2)=12
θ=45.

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