The circles `x^2+y^2-2x-4y+1=0` and `x^2+y^2+4x+4y-1=0` ............a)touch internally b)touch externally c)have `3x+4y-1=0` as the common tangent at the point of contact d)have `3x+4y+1=0` as the common tangent at the point of contact

Options

A. touch internally
B. touch externally
C. have `3x+4y-1=0` as the common tangent at the point of contact
D. have `3x+4y+1=0` as the common tangent at the point of contanct.

Answer

2,3

Explanation

For the given circles `S_(1) : x^(2)+y^(2)-2x-4y+1=0` and `S_(2) : x^(2) + y^(2)+4x+4y-1=0`
`C_(1) -= (1,2) r_(1)=2,C_(2) -= (-2,-2) , ` and `r_(2)=3`
Now, `r_(1)+r_(2)=5` and `C_(1)C_(2)=5`.
Hence, the circles touch externally. Also, the common tangent at the point of contact is `S_(1) - S_(2)=0` or `3x+4y-1=0`.