Question

Area of the triangle formed by the tangent, normal at $(1,1)$ on the curve $\sqrt{x}+\sqrt{y}=2$ and the y axis is (in sq. units)

• A. $1$
• B. $2$
• C. $\frac{1}{2}$
• D. $4$

Answer 1

The correct option is A $1$

$\frac{1}{\sqrt{x}}+\frac{y^1}{\sqrt{y}}=0$
$y^{\prime }=-\sqrt{\frac{y}{x}}$
$y^{\prime }=-1at(n=1,y=1)$
$(y-1)=-1(x-1)$
$y=2$
$(y-1)=1(x-1)$
$y=0$
$Area=\frac{1}{2}\times 2\times 1$
$=1$