Question

If $d_1$ is the distance between the lines $3x+4y+5=0$ and $6x+8y+20=0$, and $d_2$ is the distance between the lines $5x+12y+13=0$ and $10x+24y+52=0$, then $\frac{d_1}{d_2}$ equals.

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

Consider the given equations of the lines.

$3x+4y+5=0$ $..........\left(1\right)$

And $6x+8y+20=0$

$3x+4y+10=0$ $........\left(2\right)$

So, $d_1=\frac{|5-10|}{\sqrt{3^2+4^2}}$

$d_1=\frac{|-5|}{5}=1$

Since, $5x+12y+13=0$ $...........\left(3\right)$

And $10x+24y+52=0$

$5x+12y+26=0$ $...........\left(4\right)$

So, $d_2=\frac{|13-26|}{\sqrt{5^2+{12}^2}}$

$d_1=\frac{|-13|}{13}=1$

So,

$\frac{d_1}{d_2}=\frac{1}{1}=1$

Hence, this is the answer.