IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

neeraj_agarwal_1990

A straight line through the point (h, k) where h > 0 and k > 0, makes positive intercepts on the coordinate axes. Then the minimum length of the line intercepted between the coordinate axes is:

(A).	(h^{2/ 3} + k^{2/ 3})^{3 /2}	(B).	(h ^3/2 + k ^3/2)^{2/ 3}
(C).	(h^2/3 k^{2/ 3}) ^3/2	(D).	(h ^3/2 k ^3/2)^{2/ 3}

KAB

Let the equation of the line be x/a+y/b=1

Now since it passes through (h,k),

h/a+k/b=1

So a=hb/(b-k)

Length of the line intercepted between the axes is L=

(a²+b²)......(1)

ie L=

((hb/(b-k))²+b²)

Now find dL/db. For L to be minimum put dL/db=0

You will get b=(h^2/3k^1/3)+k and a=(h^1/3k^2/3)+h

Substitute the values of a and b in (1)

You will get L=(h^2/3+k^2/3)^3/2

So answer is option A)

Also tell me what are the missing symbols in options C) and D)

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