$A$ straight line moves such that the sum of the reciprocals of its intercepts on two perpendicular lines is constant. Then the line always passes through:

The coordinates of a point $P$ on the line $2x - y + 5 = 0$ such that $|PA - PB|$ is maximum,where $A$ is $(4, -2)$ and $B$ is $(2, -4)$,are:

The equation of the locus of the foot of the perpendicular drawn from the origin to a line passing through a fixed point $(a, b)$ is:

If $A=(5,3)$,$B=(3,-2)$ and a point $P$ is such that the area of the triangle $PAB$ is $9$,then the locus of $P$ represents

If $P = (1, 1)$,$Q = (3, 2)$ and $R$ is a point on the $x$-axis,then the value of $PR + RQ$ will be minimum at

$A$ frog is presently located at the origin $(0,0)$ in the $XY$-plane. It always jumps from a point with integer coordinates to a point with integer coordinates,moving a distance of $5$ units in each jump. What is the minimum number of jumps required for the frog to go from $(0,0)$ to $(0,1)$?