# NCERT Class 11 Mathematics Solutions: Chapter 10 – Straight Lines Miscellaneous Exercise 10 Part 6 (For CBSE, ICSE, IAS, NET, NRA 2022)

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1. If three lines whose equations are are concurrent show that

The equations of the given lines are

… eq (1)

… eq (2)

… eq (3)

On subtracting equation (1) from (2)

On substituting this value of in eq (1)

is the point of intersection of lines (1) and (2) .

It is given that lines (1) , (2) , and (3) are concurrent.

Hence, the point of intersection of lines (1) and (2) will also satisfy equation (3) .

2. Find the equation of the lines through the point which make an angle of with the line .

Consider the slope of the required line be .

The given line can be written as , which is of the form

Slope of the given line

It is given that the angle between the required line and line .

We know that if θ is the acute angle between lines with slopes , then

Case I:

The equation of the line passing through and having a slope of 3 is:

Case II:

The equation of the line passing through and having a slope of is:

So, the equation of the lines are .

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