Question

The length of subtangent to the curve $\sqrt{x}+\sqrt{y}=3$ at the point(4, 1) is -

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. 3
• D. 2

Answer 1

The correct option is D 2

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

Length of subtangent $=\left|\frac{y}{\frac{dy}{dx}}\right|=2$