The two points $A$ and $B$ in a plane are such that for all points $P$ lying on a circle satisfying $\frac{PA}{PB} = k$,then $k$ will not be equal to:

The locus of the midpoints of the chords of the circle $x^{2}+y^{2}=4$ which subtend a right angle at the origin is

The locus of the image of the point $(2, 3)$ in the line $(2x - 3y + 4) + k(x - 2y + 3) = 0, k \in R$ is a:

The locus of a point $(x, y)$ whose distance from the point $(-g, -f)$ is always $a$,where $k = g^2 + f^2 - a^2$,is:

What is the equation of the locus of a point which moves such that $4$ times its distance from the $x$-axis is the square of its distance from the origin?

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 $.................$.