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

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 equations of the lines through the point of intersection of the lines x – y + 1 = 0 and 2x – 3y + 5 = 0 and whose distance from the point (3, 2) is .

P₁, P₂ are points on either of the two lines at a distance of 5 units from their point of intersection. Find the coordinates of the foot of perpendiculars drawn from P₁, P₂ on the bisector of the angle between the given lines.

If p is the length of perpendicular from the origin on the line and a₂, p₂, b₂ are in A.P, then show that a₄ + b₄ = 0.