Find the points on the line x + y = 4 which lie at a unit distance from the line 4x + 3y = 10.

Find the equation of the line passing through the point of intersection 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x +4y = 7.

If the intercept of a line between the coordinate axes is divided by the point (-5, 4) in the ratio 1: 2, then find the equation of the line.

If the equation 12x²-10xy+2y²+14x-5y+c=0 represents a pair of straight lines, find the value of c. Find the separate equations of the straight lines and also the angle between them.

For what value of k does 12x²+7xy+ky²+13x-y+3=0 represents a pair of straight lines? Also write the separate equations