If the points $A(3, 4)$,$B(7, 7)$,and $C(a, b)$ are collinear and $AC = 10$,then $(a, b) =$

$A$ point $P$ on a line is at a distance of $4$ units from the origin $(0,0)$. If the line makes an angle of $60^{\circ}$ with the negative direction of the $X$-axis,then the coordinates of $P$ are

If $A=(0,1), B=(1,2), C=(-2,1)$,then the equation of the locus of a point $P(x,y)$ such that the area of triangle $PAB$ equals the area of triangle $PAC$ is:

$A$ 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:

$A$ 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 passing through a fixed point $(2,3)$ intersects the coordinate axes at points $P$ and $Q$. If $O$ is the origin and $R$ is a variable point such that $OPRQ$ is a rectangle,then the locus of $R$ is