NCERT Class 11 Mathematics Solutions: Chapter 10 – Straight Lines Miscellaneous Exercise 10 Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Different Forms for the Equation of a Line

1. Find the values of k for which the line is

(a) Parallel to the axis,

(b) Parallel to the axis,

(c) Passing through the origin.

Answer:

The given equation of line is

… eq (1)

(a) If the given line is parallel to the axis, then

Slope of the given line Slope of the x-axis

The given line can be written as

, which is of the form .

Slope of the given line

Slope of the axis

So, if the given line is parallel to the axis, then the value of .

(b)

If the given line is parallel to the axis, it is vertical.

Hence, its slope will be undefined.

The slope of the given line is is undefined at

If the given line is parallel to the y-axis, then the value of .

(c)

If the given line is passing through the origin, then point satisfies the given equation of line.

So, if the given line is passing through the origin, then the value of is either