NCERT Class 11 Mathematics Solutions: Chapter 10 –Straight Lines Miscellaneous Exercise 10 Part 2

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

Answer:

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.

Answer:

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 .