The circles `x^(2)+y^(2)+2x-2y+1=0` and `x^(2)+y^(2)-2x-2y+1=0` touch each other

Options

A. externally at (0, 1)
B. internally at (0, 1)
C. externally at (1, 0)
D. internally at (1, 0)

Answer

A

Explanation

The centres of the two circles are `C_(1)(-1, 1)` and `C_(2)(1, 1)` and both have radii equal to 1.
We have, `C_(1)C_(2)=2` and, Sum of the radii = 2. So, the two circles touch each other externally. The equation of the common tangent is obtained by subtracting the two equations.
The equation of the common tangent is
`4x=0rArr x=0`
Putting x=0 in the equation of the either circle, we get
`y^(2)-2y+1=0 rArr (y-1)^(2)=0 rArr y=1`
Hence, the points where the two circles touch is (0, 1)