Question

find the shortest distance between the lines 2y=-2x-4 and-3y=3x-6(in units)​

Answer 1

Answer:

2y=2x-4

3y=3x-6

substracting both side

-y=-x+2

Answer 2

Solution:

let, the shortest distance between the the line 2y = - 2x - 4 and -3y =3x -6 be d

here, 2y = -2x - 4 ------ 1

         -3y = 3x -6   ------2

slope of equation 1 be m1 and equation 2 be m2

now, the slope of equation 1

  2y= -2x -4

    y = -x -2

so, m1 = -1 ,       from y= mx +c    

the slope of equation 2

  -3y = 3x -6

     y = -x - 2

so m2 = -1 ,        from y= mx +c

let, M =m1= m2 = -1

we know, shortest distance of two parallel line

d = | c2 - c1 |/√ 1+ M^2

d = | -6+4 |/√ 1+ (-1)^2

d = 2/√2

d = √2

therefore, the shortest distance is √2