NCERT Class 11 Mathematics Solutions: Chapter 10 – Straight Lines Miscellaneous Exercise 10 Part 11 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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 .