If the midpoint of the line segment joining the points $(5, a)$ and $(b, 7)$ is $(3, 5)$,find $(a, b)$.

The coordinates of the points $A, B, C$ are $(x_1, y_1)$,$(x_2, y_2)$,$(x_3, y_3)$ and $D$ divides the line $AB$ in the ratio $l : k$. If $P$ divides the line $DC$ in the ratio $m : k + l$,then the coordinates of $P$ are

If the distance between the points $(a \cos \theta, a \sin \theta)$ and $(a \cos \phi, a \sin \phi)$ is $2a$,then $\theta$ is equal to

Find the slope of a line,which passes through the origin and the mid-point of the line segment joining the points $P(0, -4)$ and $B(8, 0)$.

If the coordinates of the vertices of $\Delta OAB$ are $(0, 0)$,$(\cos \alpha, \sin \alpha)$,and $(-\sin \alpha, \cos \alpha)$ respectively,then $OA^2 + OB^2 = $

What is the distance of the point $(6, 8)$ from the $x$-axis?