Ratio in Which Line Divides Segment Joining 2 Points

Q. In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4?

Q. A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio 1: n . Find the equation of the line.

Q. A rod of length $l$ moves such that its ends $A$ and $B$ always lie on the lines $3x-y+5=0$ and $y+5=0$ respectively. Then the locus of the point $P$ which divides $AB$ internally in the ratio of $2:1,$ is

1. $l^2=\frac{1}{4}(3x+3y-5{)}^2+(3y+15{)}^2$
2. $l^2=\frac{1}{4}(3x-3y+5{)}^2+(3y-5{)}^2$
3. $l^2=\frac{1}{4}(3x-3y-5{)}^2+(3y-5{)}^2$
4. $l^2=\frac{1}{4}(3x-3y-5{)}^2+(3y+15{)}^2$