Find a point on the $x$-axis,which is equidistant from the points $(7, 6)$ and $(3, 4)$.

The line $2x + y - 3 = 0$ divides the line segment joining the points $A(1, 2)$ and $B(-2, 1)$ in the ratio $a : b$ at the point $C$. If the point $C$ divides the line segment joining the points $P\left(\frac{b}{3a}, -3\right)$ and $Q\left(-3, -\frac{b}{3a}\right)$ in the ratio $p : q$,then $\frac{p}{q} + \frac{q}{p} =$

What are the coordinates of the point that divides the line segment joining the points $(-3, -4)$ and $(-8, 7)$ externally in the ratio $7 : 5$?

If the point $M(x, y)$ divides the line segment joining $A(b \cos \alpha, b \sin \alpha)$ and $B(a \cos \beta, a \sin \beta)$ in the ratio $b:a$,then $x \cos \frac{\alpha + \beta}{2} + y \sin \frac{\alpha + \beta}{2} = $

Find the coordinates of the point that divides the line segment joining the points $(-3, 2)$ and $(3, -4)$ internally in the ratio $3 : 2$.

In what ratio does the point $(8, 4)$ divide the line segment joining the points $(5, -2)$ and $(9, 6)$?