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 smallest circle passing through the point of intersection of the line x+y=1 and the circle x^(2)+y^(2)=9 .

The equation of the parabola which passes through the intersection of a line x+y=0 and the circle x^(2)+y^(2)+4 y=0 is

Find the equation of the circle passing through the intersection of the circles x^2+y^2=2ax, x^2+y^2=2by and having its centre on the line x/a-y/b=2 .

Find the equation of the circle passing through the intersection of the circles, x^2+y^2-2ax=0 and x^2+y^2-2by=0 and having the centre on the line x/a - y/b = 2.

Find the equation of the circle passing through the origin, having its centre on the line x+y=4 and intersecting the circle x^2+y^2-4x+2y+4=0 orthogonally.

Find the equation of the circle passing through the origin, having its centre on the line x+y=4 and intersecting the circle x^2+y^2-4x+2y+4=0 orthogonally.