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Home » Reduce the lines 3x – 4y + 4 = 0 and 2x + 4y – 5 = 0 to the normal form and hence find which line is nearer to the origin.
Reduce the lines 3x – 4y + 4 = 0 and 2x + 4y – 5 = 0 to the normal form and hence find which line is nearer to the origin.
CBSE | Class 11 | Exercise 23.9 | Maths | RD Sharma | Straight Lines
Reduce the lines 3x – 4y + 4 = 0 and 2x + 4y – 5 = 0 to the normal form and hence find which line is nearer to the origin.

Given:

The normal forms of the lines:

    \[3x\text{ }-\text{ }4y\text{ }+\text{ }4\text{ }=\text{ }0\]

And

    \[~2x\text{ }+\text{ }4y\text{ }-\text{ }5\text{ }=\text{ }0.\]

To find, in given normal form of a line, which is nearer to the origin.

    \[-3x\text{ }+\text{ }4y\text{ }=\text{ }4\]

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 41

Now

    \[2x\text{ }+\text{ }4y\text{ }=\text{ }\text{ }5\]

    \[-2x\text{ }\text{ }4y\text{ }=\text{ }5\]

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 42

From both the equations (1) and (2):

    \[45\text{ }<\text{ }525\]

∴ The line :

    \[3x\text{ }-\text{ }4y\text{ }+\text{ }4\text{ }=\text{ }0\]

is nearer to the origin.

 

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