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Question

If the circles x2+y2=a and x2+y26x8y+9=0, touch externally, then a=



A

1

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B

-1

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C

21

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D

16

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Solution

The correct option is A

1


x2+y2=a (1)
and x2+y26x8y+9=0 (2)

Let circles (1) and (2) touch each other at point P.

The centre of the circle x2+y2=a,Ois(0,0)

The centre of the circle x2+y26x8y+9=0, is (3, 4)

Also, radius of circle (1)=a=OP

Radius of circle
(2)=9+169=4=C1P

From figure, we have :
CO=C1P+OP

32+42=4+a

5=4+a

a=1



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