Find the equation of the smallest circle passing through the intersection of the line `x+y=1` and the circle `x^2+y^2=9`

Find the equation of the circle passing through the point of intersection of the lines x+3y=0 and 2x-7y=0 and whose centre is the point of intersection of the lines x+y+1=0 and x-2y+4=0

Find the equation of the circle having (1,-2) as its centre and passing through the intersection of the lines 3x+y=14 and 2x+5y=18

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 3x-y=1 and 5x+2y=9 and parallel to the line 3x+5y=8 .

Find the equation of a line passing through the intersection of the lines 3x+2y=5 and 2x-y=1 and cuts equal intercepts on the axes.

Find the equations of the circles passing through the point (-4,3) and touching the lines x+y=2 and x-y=2

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

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.