The line equation is $\"\"$ .

The equation of parabola is $\"\"$ .

Consider the distance between the line and the parabola be $\"\"$ .

Hence $\"\"$ .

The distance is maximum when its first derivative becomes zero.

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

$\"\"$

Equate $\"\"$ to zero.

$\"\"$

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

$\"\"$

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

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