NCERT Class 11 Mathematics Solutions: Chapter 10 – Straight Lines Miscellaneous Exercise 10 Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Forms for the Equation of a Line

1. Find the equation of the line parallel to axis and drawn through the point of intersection of the lines .


The equation of any line parallel to the axis is of the form

… eq (1)

The two given lines are

… eq (2)

… eq (3)

On solving equations (2) and (3) ,

We obtain

So, is the point of intersection of lines eq (2) and (3)

Line passes through point .


The required equation of the line is

2. Find the equation of a line drawn perpendicular to the line through the point, where it meets the axis.


The equation of the given line is

This equation can also be written as

, which is of the form

slope of the given line

Slope of line perpendicular to the given line

Consider the given line intersect the axis at .

On substituting with in the equation of the given line,

The given line intersects the axis at .

The equation of the line that has a slope of and passes through point is

So, the required equation of the line is .