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. 1/2
• D. 4

Answer 1

The correct option is A 1

REF.image

$0\to$slope of tangent = $y^1$ ; slope of normal $=-1/y^1$

$\sqrt{x}+\sqrt{y}=2\Rightarrow \frac{1}{2\sqrt{x}}+\frac{y^1}{2\sqrt{y}}=0\Rightarrow y^1=-\sqrt{\frac{y}{x}}=-1$

$\underset{–}{Tangent}:-y-1=-1(x-1)\Rightarrow y-1=1-x\Rightarrow x+y=2$

$\underset{–}{Normal}:-y-1=1(x-1)\Rightarrow y=x$

$\Rightarrow$Area of triangle $=\frac{1}{2}\times$ base $\times$ height

$=\frac{1}{2}\times 2\left(1\right)=1\Rightarrow \left(A\right)$