NCERT Class 11 Mathematics Solutions: Chapter 10 –Straight Lines Miscellaneous Exercise 10 Part 11

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The distance point and line

The Distance Point and Line

The distance point and line

1. If sum of the perpendicular distances of a variable point from the lines and is always . Show that P must move on a line.

Answer:

The equations of the given lines are

…………… eq (1)

………………. eq (2)

The perpendicular distances of from lines (1) and (2) are respectively given by

It is given that

[Assuming are positive]

Which is the equation of a line.

Similarly, we can obtain the equation of line for any signs of

Thus, point P must move on a line.

2. Find equation of the line which is equidistant from parallel lines .

Answer:

The equations of the given lines are

………………eq (1)

……………….. eq (2)

Consider be the arbitrary point that is equidistant from lines (1) and (2).

The perpendicular distance of from line (1) is given by

The perpendicular distance of from line (2) is given by

Since P (h, k) is equidistant from lines (1) and (2),

The case is not possible as

(which is absurd)

The required equation of the line is .