Question

The length of subtangent to the curve $\sqrt{x}+\sqrt{y}=7$ at the point $(16,9)$ is

• A. 4
• B. 8
• C. 12
• D. 16

Answer 1

The correct option is C 12

${\begin{array}{c}\frac{1}{2}\sqrt{x}+\frac{1}{2\sqrt{y}}.y^{\prime }=0\Rightarrow y^{\prime }=-\frac{\sqrt{y}}{\sqrt{x}}\end{array}|}_{(16,9)}=\frac{-3}{4}$
Length of subtangent $\Rightarrow \left|\frac{y}{\frac{dy}{dx}}\right|=\left|\frac{9}{\frac{-3}{4}}\right|=12$