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Find the required point be `P(x_1, y_1)dot`The tangent to the curve `sqrt(x)+sqrt(y)=4`at which tangent is equally inclined to the axes. |
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Answer» We have, `sqrt(x) + sqrt(y)=4` `rArr x^(1//2)+y^(1//2)=4` `rArr 1/2.1/(x^(1//2))+1/2.(1/y^(1//2)).(dy)/(dx)=0` `(dy)/(dx) = -1/2.x^(-1//2)2.y^(1//2)` `=-sqrt(y/x)` Since, tangent is equally inclined to the axes. `therefore (dy)/(dx) = +-1` `rArr y/x = 1 rArr y=x` From Eq. (i), `sqrt(y)+sqrt(y)=4` `rArr 2sqrt(y)=4` `therefore y=4` and x=4 When y=4, then x=4 So, the required conditions are (4,4). |
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