Question

Let the perpendiculars 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
$2x+11y=5beP(\frac{5-11h}{2},h)Now,P=\left|\frac{12(5-11h)+7h-20}{\sqrt{625}}\right|=\left|\frac{40-125h}{25}\right|=\left|\frac{8-25h}{5}\right|P^{\prime }=\left|\frac{2(5-11h)-3h-2}{\sqrt{25}}\right|=\left|\frac{8-25h}{5}\right|\therefore P=P^{\prime }$