Question

Find the equations of the bisectors $B_1$ and $B_2$ between the lines $3x-4y+5=0$ and $5x+12y-1=0$. If $B_1$ meets the axes of coordinates in $A$ and $B$ whereas $B_2$ meets in $C$ and $D$ then find the ratio $AC:DB$.

Answer 1

The two bisectors as usual are

$B_1,16x+2y+15=0\therefore A(-\frac{15}{16},0),B(0,-\frac{15}{2})$

$B_2,x-8y+5=0$

$C(-5,0),D(0,5/8)$

$\therefore AC=5-\frac{15}{16}=\frac{65}{16}$

$DB=\frac{5}{8}+\frac{15}{2}=\frac{65}{8}$

$\therefore AC:DB=\frac{8}{16}=\frac{1}{2}or1:2$