Q21 of 292 Page 506

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.

(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)


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