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Question

Which of the following line(s) is nearest to origin

A
4x3y+12=0
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B
3x3y+12=0
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C
3x4y+4=0
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D
3x+4y+5=0
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Solution

The correct option is C 3x4y+4=0
Distance of origin from the line ax+by+c=0 will be |c|a2+b2 units
so,
(i)distance of the line 4x3y+12=0 from the origin
=125units

(ii)distance of the line 3x3y+12=0 from the origin
=1232=22units

(iii)distance of the line 3x4y+4=0 from the origin
=45units

(iv)distance of the line 3x4y+5=0 from the origin
=1units
line 3x4y+4=0 will be nearest to origin

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