InterviewSolution
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InterviewSolution
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If the sum of thesquares of the intercepts on the axes cut off by tangent to the curve `x^(1/3)+y^(1/3)=a^(1/3), a >0`at `(a/8, a/8)`is 2, then `a=`1 (b) 2(c) 4 (d) 8A. 1B. 2C. 4D. 8 |
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Answer» Correct Answer - C We have, ` x^(1//3) + y^(1//3)= a^(1//3) ` ` rArr (1)/(3)x^(2//3)+(1)/(3)y^(-2//3)(dy)/(dx)=0 ` ` rArr (dy)/(dx)=-(x^(-2//3))/(y^(-2//3))= -(x^(2//3))/(y^(2//3)) rArr ((dy)/(dx))_((a//8 "," a//8))=-1 ` The equation of the tangent at `(a//8 ,a//8)` is given by ` y-(a)/(8)=-1(x-(a)/(8)) rArr x+y-(a)/(4)=0 ` The x and y intercepts of this line on the coordinate axes are each equal to ` a//4. ` So, we have `((a)/(4))^(2)+((a)/(4))^(2)=2 rArr a=4 ` |
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