Question

Let the perpendicular from any point on the line $2x+11y=5$ upon the lines $24x+7y=20$ and $4x-3y=2$ have the lengths $p$ and $p^{\prime }$ respectively. Then

• A. $2p=p^{\prime }$
• B. $p=p^{\prime }$
• C. $p=2p^{\prime }$
• D. none of these

Answer 1

Answer: (B)

$p=p^{\prime }$

let any point on line $2x+11y=5$ be $P(\frac{5-11h}{2},h)$

now, $p=\left|\frac{12(5-11h)+7h-20}{\sqrt{625}}\right|=\left|\frac{40-125h}{25}\right|=\left|\frac{8-25h}{5}\right|$

and $p^{\prime }=\left|\frac{2(5-11h)-3h-2}{\sqrt{25}}\right|=\left|\frac{8-25h}{5}\right|$

Therefore, $p=p^{\prime }$