An enemy jet is flying along the curve . A soldier is placed at the point (3, 2). Find the nearest point between the soldier and the jet.

Question

Philoid · Accepted Answer

(1, 3)

Let P(x,y) be the position of the jet and the soldier is placed at A(3,2)

AP=

As y=x²+2 or y-2=x²

؞ AP²=(x-3)² + x⁴=z (say)

؞ 2x-6+4x³=0

Put x=1

2-6+4=0

؞ x-1 is a factor

And

or x=1

(at x=1)>0

؞ z is minimum when x=1,y=1+2=3

Point is (1,3)