The equations of the parabolas are $\"\"$ and $\"\"$ .

Consider the distance between the two parabolas be $\"\"$ .

Hence $\"\"$ .

$\"\"$

The distance is minimum when its first derivative becomes zero.

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

Equate $\"\"$ to zero.

$\"\"$

Substitute $\"\"$ in $\"\"$ .

$\"\"$

Therefore the minimum vertical distance is $\"\"$ .

The minimum vertical distance is $\"\"$ .