InterviewSolution
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InterviewSolution
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A variable line `x/a + y/b = 1` moves in such a way that the harmonic mean of a and b is 8. Then the least area of triangle made by the line with the coordinate axes is(1) 8 sq. unit(2) 16 sq. unit(3) 32 sq. unit(4) 64 sq. unitA. 8 sq. unitB. 16 sq. unitC. 32 sq. unitD. 64 sq. unit |
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Answer» Correct Answer - C Given line is `(x)/(a)+(y)/(b)=1` It meets the axes at point A(a,0) and B(0,b). Area of triangle AOB, `Delta = (1)/(2)` ab Given that 8 is H.M. of a and b. `therefore (1)/(a)+(1)/(b)=(1)/(4)` `rArr b = (4a)/(a-4)` `therefore Delta = (2a^(2))/(a-4)` Differentiating w.r.t. a, we get ` (dDelta)/(da) = 2(2a(a-4)-a^(2))/((a-4)^(2))` `rArr (dDelta)/(da) = (2a(a-8))/((a-4)^(2))` `"If " (dDelta)/(da) = 0, "then " a =8` This is the value of a for which area is minimum `therefore Delta_(min.) = 32 " sq.units."` |
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