NCERT Class 11 Mathematics Solutions: Chapter 10 – Straight Lines Miscellaneous Exercise 10 Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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1. Find the values of θ and p, if the equation is the normal form of the line .

The equation of the given line is

This equation can be reduced as

On dividing both sides by

… eq (1)

Comparing equation (1) to

The values of are negative,

So, the respective values of .

3. Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are , respectively.

Consider the intercepts cut by the given lines on the axes be .

It is given that

… (1)

… (2)

On solving equations (1) and (2) , we obtain

or

It is known that the equation of the line whose intercepts on the axes are is

Or

Case I

In this case, the equation of the line is

.

Case II:

In this case, the equation of the line is .

Thus, the required equation of the lines are .