Question

If$L_1=0$ and $L_2=0$ be two intersecting straight lines, the number of points, whose distance from $L_1$ is $2$ units and from$L_2$ is $5$ units is

• A. $1$
• B. $0$
• C. $4$
• D. infinite

Answer 1

The correct option is C

$4$

Explanation for the correct answer:

Let $L_1=0$ and $L_2=0$ be two intersecting lines

The locus of all points at a distance of $2$ units from the line $L_1=0$ is $2$ parallel lines, one on either side of the given line at a perpendicular distance of $2$ units.

Similarly,

The locus of all points at a distance of $5$ units from the line $L_2=0$ is $2$ parallel lines, one on either side of the given line at a perpendicular distance of $5$ units.

When we represent these loci on the a graph, we can observe that these loci intersect each other at $4$ points.

Each of these points is at a distance of $2$ units from $L_1=0$ and and $5$ units from $L_2=0$.

The solid lines represent $L_1=0$ and $L_2=0$ and the broken lines represent the loci. Th points of intersection of the loci are marked out as well.

Hence, when two lines intersect each other then there are $4$ points at a distance of $2$ units and $5$ units from them,

Hence, option (C) is the correct answer.