If a circle passing through $A(1,1)$ touches the $X$-axis, then the locus of the other end of the diameter through $A$ is

If $C(\alpha, \beta)(a<0)$ is the centre of the circle that touches the $Y$-axis at $(0,3)$ and makes an intercept of length 2 units on positive $X$-axis, then $(\alpha, \beta)=$

The equations of the tangents to the circle $x^2+y^2=4$ drawn from the point $(4,0)$ are

The image of every point lying on the curve $x^2+y^2=1$ in the line $x+y=1$ satisfies the equation