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Question

Consider the circles x2+y2+2ax+c=0 and x2+y2+2by+c=0. The two circles touch each other if.

A
c=a2+b2
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B
1c=1a2+1b2
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C
c=1a2+1b2
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D
c=1a2+b2
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Solution

The correct option is B 1c=1a2+1b2
let ,S1=x2+y2+2ax+c , center = (a,0)
S2=x2+y2+2by+c , center = (0,b)

we know that circles touches each other,

sun of radii is equal to distance between their centers

r1+r2=a2+b2

a2c+b2c=a2+b2

we can have ,

1c=1a2+1b2

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