Center of a circle S passing through the intersection points of circles `x^2+y^2-6x=0 &x^2+y^2-4y=0` lies on the line `2x-3y+12=0` then circle S passes through

The locus of the centre of the circle passing through the intersection of the circles x^(2)+y^(2)=1 and x^(2)+y^(2)-2x+y=0 is

Find the equation of the circle passing through the intersection of the circles x^(2)+y^(2)-4=0 and x^(2)+y^(2)-2x-4y+4=0 and touching the line x+2y=0

Find the equation of a line passing through the intersection of the lines x+3y=4 and 2x-y=1 and (0,0) lies on this line.

Find the equation of the circle passing through the point of intersection of the circles x^(2)+y^(2)-6x+2y+4=0,x^(2)+y^(2)+2x-4y-6=0 and with its centre on the line y=x

The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x^(2)+y^(2)=9 , is

" The equation of smallest circle passing through intersection of curve " x^(2)+y^(2)-4x-2y-2=0 " and line " x+y-5=0 " is