Find the point ofintersection of the tangents drawn to the curve `x^2y=1-y`at the points whereit is intersected by the curve `x y=1-ydot`A. `(0,-1)`B. `(1,1)`C. `(0,1)`D. none of these

Find the point ofintersection of the tangents drawn to the curve `x^2y

1.	Find the point ofintersection of the tangents drawn to the curve `x^2y=1-y`at the points whereit is intersected by the curve `x y=1-ydot`A. `(0,-1)`B. `(1,1)`C. `(0,1)`D. none of these
Answer» Correct Answer - C Solving the two equations, we get ` x^(2)y =xy rArr xy(x-1)=0 rArr x=0, y=0, x=1 ` Since y = 0 does not satisfy the two equations. So, we neglect it. Putting x = 0 in the either equation, we get x = 1. Now, putting x=1 in one of the two equations we obtain ` y= 1//2. ` Thus, the two curves intersect at (0,1) and `(1,1//2).` Now, ` x^(2)y=1-y rArr x^(2)(dy)/(dx) + 2xy = -(dy)/(dx) rArr (dy)/(dx) =-(2xy)/(x^(2)+1) ` ` rArr ((dy)/(dx))_((0","1)) =0 " and " ((dy)/(dx))_((1"," 1//2))=-(1)/(2)` The equations of the required tangents are ` y-1 =0(x-0) " and " y-(1)/(2)=(-1)/(2)(x-1) ` ` rArr y=1 " and " x+2y-2=0 ` These two tangents intersect at (0,1)

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Find the point ofintersection of the tangents drawn to the curve `x^2y=1-y`at the points whereit is intersected by the curve `x y=1-ydot`A. `(0,-1)`B. `(1,1)`C. `(0,1)`D. none of these

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