NCERT Class 11 Mathematics Solutions: Chapter 10 –Straight Lines Miscellaneous Exercise 10 Part 4

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Forms for the equation of a line

Forms for the Equation of a Line

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 .

Answer:

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 .

So,

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.

Answer:

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 .