What is the distance between the points which divide the line segment joining (4, 3) and (5, 7) internally and externally in the ratio 2 : 3 ?

What is the angle between the straight lines $$({m^2} - mn)y = (mn + {n^2})x + {n^3}$$ and $$(mn + {m^2})y = (mn - {n^2})x + {m^3}$$, where m > n?

What is the equation of the straight line cutting-off an intercept 2 from the negative direction of Y-axis and inclined at 30$$^\circ$$ with the positive direction of X-axis?

What is the equation of the line passing through the point of intersection of the lines $$x + 2y - 3 = 0$$ and $$2x - y + 5 = 0$$ and parallel to the line $$y - x + 10 = 0$$ ?