For the circle $x^2 + y^2 + 3x + 3y = 0$,which of the following relations is true?

If the equation of the circle passing through the points $(-1,0), (-1,1), (1,1)$ is $ax^2+ay^2+2gx+2fy-2=0$,then $a=$

The sides of a rectangle are given by the equations $x=-2, x=4, y=-2$ and $y=5$. Then the equation of the circle,whose centre is the point of intersection of the diagonals,lying within the rectangle and touching only two opposite sides,is

The number of integral values of $\lambda$ for which $x^2 + y^2 + \lambda x + (1 - \lambda)y + 5 = 0$ is the equation of a circle whose radius cannot exceed $5$ is:

The centre of the circle passing through the point $(0,1)$ and touching the curve $y=x^2$ at $(2,4)$ is

In a square $ABCD$ of side length $a$,suppose $AB$ and $AD$ are along the coordinate axes. Then,the circle that circumscribes the square is