Question

Distance between the lines 3x+2y=6 and 3x+2y=12 is

Answer 1

Answer:

3x+2y=6 and 3x+2y=12

3xy=2-6 and 3xy=2-12

3xy= 4 and 3xy= 10

xy= 4/3 and xy= 10/3

xy= 0.75 and xy= 0.3

so,it's not equal

Answer 2

Given : 3x+2y=6 and 3x+2y=12 is

To find : Distance between the lines

Solution:

3x+2y=6

3x+2y=12 is

slope is -3/2

so slope of line having shortest distance would be  2/3

y =  2x/3  + c₁

or  

3y  = 2x + c

Let say take a point   x  = 0  on  3x+2y=6

=> y = 3

( 0 , 3) is the point on 3y  = 2x + c

=> 9 = c

=> 3y = 2x + 9

solve

3y = 2x + 9  => 9y = 6x + 27

3x+2y=12  =>  6x + 4y = 24

=> 13y  = 51

=> y = 51/13  ,   x = 18/13

Distance = (0. 3)    ( 18/13 , 51/13)

= √(18/13 - 0)² + (51/13 - 3)²

=  (1/13)√(18² + 12²)

= (6/13)√(3² + 2²)

=  (6/13)√13

= 6/√13

6/√13  is the distance .

Another method : using direct formula

d = |12 -6|/√[3² +2²]

=> d = 6/√13

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