# NCERT Class 11 Mathematics Solutions: Chapter 10 – Straight Lines Miscellaneous Exercise 10 Part 7 (For CBSE, ICSE, IAS, NET, NRA 2022)

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1. Find the equation of the line passing through the point of intersection of the lines and that has equal intercepts on the axes.

Answer:

Consider the equation of the line having equal intercepts on the axes be

Or

… eq (1)

On solving equations ,

is the point of intersection of the two given lines.

Since equation (1) passes through point,

Equation (1) becomes

So, the required equation of the line is

2. Show that the equation of the line passing through the origin and making an angle with the line is

Answer:

Consider the equation of the line passing through the origin be .

If this line makes an angle of with line , then angle is given by

Case I:

Case II:

So, the required line is given by .