Question

A straight line through origin O meets the lines $3y=10-4x$ and $8x+6y+5=0$ at points A and B respectively. Then O divides the segment AB in the ratio:

• A. $2:3$
• B. $1:2$
• C. $4:1$
• D. $3:4$

Answer 1

Answer: (C)

$4:1$

The lines $4x+3y-10=0$ and $8x+6y+5=0$ , are parallel as

$\frac{4}{8}=\frac{3}{6}$

Now length of perpendicular from $(0,0)$ to $4x+3y-10=0$ is,

$P_1=\left|\frac{4\times 0+3\times 0-10}{\sqrt{4^2+3^2}}\right|=\frac{10}{5}=2$

Length of perpendicular from $(0,0)$ to $8x+6y+5=0$ is

$P_2=\left|\frac{8\times 0+6\times 0+5}{\sqrt{6^2+8^2}}\right|=\frac{5}{10}=\frac{1}{2}$

$\therefore P_1:P_2=2:\frac{1}{2}=4:1$