Correct option (a) externally at (0, 1)
Explanation:
The equation of circle of the form
x2 + y2 + 2gx + 2fy + c = 0 has centre C (− g, − f)
Therefore, the centre of the circle
x2 + y2 + 2x − 2y + 1 = 0 is C1 (−1, 1)
x2 + y2 + 2x − 2y + 1 = 0 is C1 (−1, 1) and centre of the circle x2 + y2 − 2x − 2y + 1 = 0 is C2 (1, 1) and both have radii equal to 1. We have
Sum of radii = 1 + 1 = 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
Putting x = 0 in the equation of the either circle, we get
Hence, the points where the two circles touch is (0, 1).