If a point $P$ is equidistant from the points $A(a + b, b - a)$ and $B(a - b, a + b)$,find the locus of $P$.

The coordinates of the points $A$ and $B$ are $(a, 0)$ and $(-a, 0)$ respectively. If a point $P$ moves such that $PA^2 - PB^2 = 2k^2$,where $k$ is a constant,then the equation to the locus of the point $P$ is:

$A (a, 0)$ and $B (-a, 0)$ are two fixed points of $\Delta ABC$. If the vertex $C$ moves such that $\cot A + \cot B = \lambda$,where $\lambda$ is a constant,then what is the locus of point $C$?

$A$ particle is projected vertically upwards. If it has to stay above the ground for $12 \text{ seconds}$, then:

$A$ line cuts the $X$-axis at $A(5,0)$ and the $Y$-axis at $B(0,-3)$. $A$ variable line $PQ$ is drawn perpendicular to $AB$ cutting the $X$-axis at $P$ and the $Y$-axis at $Q$. If $AQ$ and $BP$ meet at $R$, then the locus of $R$ is

$A$ light ray emerging from a point source at $A(2,3)$ is reflected on the $Y$-axis at point $B$ and passes through point $C(5,10)$. Then the coordinates of $B$ are: