Find the equation of the line passing through the point (5, 2) and perpendicular to the line joining the points (2, 3) and (3, -1).

Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120^o with the positive direction of x-axis.

Find the equation of the straight line passing through intersection of the straight lines 5x - 6y = 1 and 3x + 2y + 5 = 0 and perpendicular to the straight line 3x - 5y + 11=0.

Show that 9x² + 24xy +16y² +21x +28y +6 = 0 represents a pair of parallel straight lines and find the distance between them.

Show that 3x²+10xy+8y²+14x+22y+15=0 represents a pair of straight lines and the angle between them is tan^-1\(\left( \frac { 2 }{ 11 } \right) \).