Question

The point of intersection of the tangents drawn to the curve $x^{2}y=1-y$ at the points where it is met by the curve $xy=1-y$ is given by

• A. $(0,-1)$
• B. $(1,1)$
• C. $(0,1)$
• D. $(1,\infty )$

Answer 1

Answer: (C)

$(0,1)$

$x^{2}y=xy$
$y=1,x=0$
$y{=}^1{/}_2,x=1$
$2x\frac{dx}{dy}=-\frac{-1}{y^2}$
$\frac{dy}{dx}=-2x{y}^2$
$(x=0)$
$\frac{dy}{dx}=0$
$(y-1)=x-0$
$y=1$ ------- (1)
$(y-\frac{1}{2})=\frac{-1}{2}(x-1)$ -----(2)
$x=0$ (By (1) & (2))
$(0,1)$