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

Options

A. `-4//3`
B. 0
C. 1
D. `4//3`

Answer

1,4

Explanation

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)`