Property 5:The equation of family of circle which touches `(y-y_1)=m(x-x_1)` at `(x_1;y_1)` for any finite m is

The equation of a circle which touches the line y = x at (1 , 1) and having y = x -3 as a normal, is

Property 4: The equation of the family of circles passing through two given points P(x_(1),y_(1)) and Q(x_(2),y_(2))

Find the equation of the circle which touch the line 2x-y=1 at (1,1) and line 2x+y=4

Find the equation of the family of circles touching the lines x^(2)-y^(2)+2y-1=0

The equation of the circle which touches both axes and whose centre is (x_(1), y _(1)) is

The equation of one of the circles which touch the pair of lines x^(2)-y^(2)+2y-1=0 is

The equation of the circle which has a tangent 2x-y-1=0 at (3, 5) on it and with the centre on x+y=5 , is

The equation of circle which touches X and Y - axes at the points (1,0) and (0,1) respectively is

The locus of the centres of circles which touches (y-1)^(2)+x^(2)=1 externally and also touches X-axis is