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If the circles x^2+y^2-9=0 and x^2+y^2+2...

If the circles `x^2+y^2-9=0` and `x^2+y^2+2a x+2y+1=0` touch each other, then `alpha` is `-4/3` (b) 0 (c) 1 (d) `4/3`

A

`-4//3`

B

0

C

1

D

`4//3`

Text Solution

Verified by Experts

The correct Answer is:
1,4
The equation of the radical axis is
`2 alpha x +2y+10=0`
i.e., `alpha x +y+5=0` (i)
Putting the value of y from (i) in the circle `x^(2)+y^(2)=9`, we get
`(1+alpha^(2))x^(2)+10 alpha x +16 =0`
Radical axis is trangent . So,
`D=0`
or `36alpha^(2)-64=0`
or `alpha = +- (4)/(3)`
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