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

The correct option is B $p=p^{\prime }$

The angle bisector of $24x+7y=20$ and $4x-3y=2$ is given by :

$\frac{24x+7y-20}{25}=\pm \frac{4x-3y-2}{5}$
On simplifying we get,

$24x+7y-20=\pm (20x-15y-10)$

$2x+11y-5=0$ or $22x-4y-5=0$

Hence, the given line is the angle bisector of the two lines. Hence, $p=p^{\prime }$