Warzone

Let us consider a parametric point $(\large h,h^{2}+2)$ on the parabola.

Equation of Tangent at that point is given by:-

$\large y+h^{2}-2xh-2=0$

So equation of Normal at that point is given by:-

$\large\frac{y-h^{2}-2}{1} = \frac{x-h}{-2h}$

Making this normal pass through $(3,2)$ we have :-

$\large 2h^{3}=3-h$

As we can very well see....the only solution is $h=1$ .

So the point on the parabola which is at the shortest distance is $(1,3)$ .

So calculating the distance from $(1,3)$ to $(3,2)$ we have it equal to $\sqrt{5}$

So our answer is $5$ .

PS(There is also an error with the problem as to solve the distance between the man on the ground and the airplane.....we also would need the height at which the plane is at. If instead of a plane , a tank or a jeep was used then it would have fit the narrative of the problem as well as it would have made the problem more accurate)

$Nice Problem$ Solved it in 2nd time...Well WAR ZONE is completed May I ask where is DRAGON QUEST and jail break?