If the sum of the distances of a point from the origin and the line $x = 2$ is $4$,then its locus is

$A$ variable circle passes through a fixed point $A(p, q)$ and touches the $x$-axis. The locus of the other end of the diameter passing through $A$ is:

The locus of the centre of circles passing through $(a, b)$ and cutting the circle $x^2+y^2-2x+4y-4=0$ orthogonally is

The locus of the point of intersection of the tangents to the circle $x^2+y^2=a^2$ which make complementary angles with the $X$-axis is

The set of all points that are at a distance of at least $2$ units from $(-3, 0)$ is

Let the point $(p, p+1)$ lie inside the region $E = \{(x, y) : 3-x \leq y \leq \sqrt{9-x^2}, 0 \leq x \leq 3\}$. If the set of all values of $p$ is the interval $(a, b)$,then $b^2+b-a^2$ is equal to $.................$.