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

Find the coordinates of the point at which the circles x^(2)-y^(2)-4x-2y+4=0 and x^(2)+y^(2)-12x-8y+36=0 touch each other.Also,find equations of common tangents touching the circles the distinct points.

If the circles x^(2)+y^(2)-8x-2y+8=0 and x^(2)+y^(2)-2x+6y+6=0 touch each other and Q(x,y) is the point of contact then Qx + Qy =

The circles x^(2)+y^(2)-12x-12y=0 and x^(2)+y^(2)+6x+6y=0 .touch each other externally touch each other internally intersect at two points none of these

Prove that the circle x^(2)+y^(2)+2x+2y+1=0 and circle x^(2)+y^(2)-4x-6y-3=0 touch each other.

Show that the circles x ^(2) + y ^(2) - 2x =0 and x ^(2) + y ^(2) - 8x + 12=0 touch each other externally. Find the point of contact.

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

If the circles x^(2)+y^(2)+2gx+2fy=0and x^(2)+y^(2)+2g'x+2f'=0 touch each other then prove that f' f = fg .