$A$ 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:

$A$ straight line $L$ with negative slope passes through the point $(1,1)$ and cuts the positive coordinate axes at the points $A$ and $B$. If $O$ is the origin,then the minimum value of $OA + OB$ as $L$ varies,is

$A$ 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 $(0,1)$?

$A$ moving line intersects the lines $x+y=0$ and $x-y=0$ at the points $A$ and $B$ respectively,such that the area of the triangle with vertices $(0,0)$,$A$,and $B$ has a constant area $C$. The locus of the mid-point of $AB$ is given by the equation:

If $P = (1, 0)$,$Q = (-1, 0)$,and $R = (2, 0)$ are three given points,then the locus of the points $S$ satisfying the relation $SQ^2 + SR^2 = 2 SP^2$ is :

$A$ straight line $L$ cuts both the lines $5x - y - 4 = 0$ and $3x + 4y - 4 = 0$. The segment of $L$ between the two lines is bisected at the point $(1, 5)$. The equation of $L$ is