If each ai>0, then the shortest distance between the point(0,-3) and the curve y=1+a1x2 + a2x4 + ...........................................+anx2n is
a) 1
b) 2
c) 3
d) 4
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1 Answers
66The distance of an arbitrary point (x,y) of the curve from (0,-3) is
d=\sqrt{x^2+(y+3)^2}=\sqrt{x^2+(4+a_1x^2+\ldots+ a_nx^{2n})^2}
since y=1+a_1x^2+a_2x^4+\ldots +a_nx^{2n}. Since all the a_i's are positive and the squares of real numbers are always non-negative, d will be minimum only when x=0. As such the shortest distance is 4.
Sushovan Halder thanks sir.
Upvote·0· Reply ·2014-07-10 05:54:32