Question

$p_1,p_2$ are the lengths of the perpendiculars from any point on $2x+11y=5$ upon the lines $24x+7y=20,4x-3y=2,$ then $p_1=$

• A. $p_2$
• B. $2p_2$
• C. $\frac{1}{2}{p}_2$
• D. $\frac{1}{3}{p}_2$

Answer 1

The correct option is A $p_2$

Let $(\frac{5}{2},0)$ the point that lies on $(2x+11y=5)$

So, $p_1=\left|\frac{(24\times \frac{5}{2}+7\times 0-20)}{25}\right|$

$p_1=\left|\frac{40}{25}\right|=\frac{8}{5}$

And similarly,
$p_2=\left|\frac{4\times \frac{5}{2}-3\times 0-2}{5}\right|$

$p_2=\left|\frac{8}{5}\right|$

So, $p_1=p_2$