If the sum of the distance of a moving point in a plane from the axis is 1, then find the locus of the point.

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 the straight line which passes through the intersection of the straight lines 2x + Y= 8 and 3x - 2y + 7 = 0 and is parallel to the straight line 4x+ y-11 =0.

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 line which passes through the point (- 4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5: 3 by this point.

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.

Find the equation of the straight line which passes through the point (1, -2) and cuts off equal intercepts from axes.

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

The line 2x - y = 5 turns about the point on it, whose ordinate and abscissae are equal, through an angle of 45° in the anti-clockwise direction. find the equation of the line in the new position.

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