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Question -

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.



Answer -

The normal forms ofthe lines 3x − 4y + 4 = 0 and 2x + 4y − 5 = 0.

Let us find, in givennormal form of a line, which is nearer to the origin.

-3x + 4y = 4

Now 2x + 4y = – 5

-2x – 4y = 5

From equations (1) and(2):

45 < 525

 The line 3x − 4y+ 4 = 0 is nearer to the origin.

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