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Question

If the circles x2+y2+2ax+c=0 and x2+y2+2by+c=0 touch each other then

A
a2+b2=c1
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B
a2+b2=c2
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C
a+b=2c
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D
1a+1b=2c
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Solution

The correct option is A a2+b2=c1
Given circles are C1:x2+y2+2ax+c=0 and C2:x2+y2+2by+c=0.

C1(a,0) and r1=a2c
C2(b,0) and r1=b2c
Since, circles touch each other
C1C2=r1+r2
|ab|=a2c+b2c
a2+b22ab=a2c+b2c+2a2cb2c
cab=a2b2c(a2+b2)+c2
a2+b2=c1
Ans: A

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