The circles `x^(2)+y^(2)-2x-4y+1=0` and `x^(2)+y^(2)+4y-1 =0`

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 contact.

Answer

B, C

Explanation

The circles …………..
`S_(1)=x^(2)+y^(2)-2x-4y+1=0` ………..(1)
`S_(2)=x^(2)+y^(2)+4x+4y-1=0` ……… (2)
`c_(1)-=(1, 2)` , `r_(1)=2`
`c_(2)-= (-2, -2)` , `r_(2) = 3`
`c_(1)c_(2) = sqrt(9+16)`
`c_(1)c_(2)=r_(1)+r_(2)`
Hene circle touch each other extermally

Equation of tangent at point of contact
`S_(1)-S_(2)=0`
`6x+8y-2=0`
`3x+4y-1=0`