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Question

If the circles x2+y2=c2 and x2+y2+2ax=0 touch each other, then

A
they touch each other externally
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B
they touch each other internally
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C
4c2=a
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D
2a2=c2
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Solution

The correct option is B they touch each other internally
Given, C1:x2+y2=c2.
Here, the center is C1(0,0) and radius r1=c.
Also, C2:x2+y2+2ax=0
(x+a)2+y2=a2
Center C2(a,0) and radius r2=a
The distance between the centres of the two circles is given by C1C2=a.
Sum of the radii of the two circles =a+c.
As the sum of the two radii is greater than the distance between the centres of the two circles, the two circles cannot touch each other externally.
Hence, the two circles touch internally,
C1C2=ca
2a=c
4a2=c2
Hence, option B is correct

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