Question

The sum of the intercepts on the coordinate axis by any tangent to the curve $\sqrt{x}+\sqrt{y}=2$ is

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

The correct option is B $4$

Let $x=4{\cos }^4\theta$ and $y=4{\sin }^4\theta$

$\Rightarrow \frac{dy}{dx}=-{\tan }^2\theta$

Equation of the tangent at $(4{\cos }^4\theta ,4{\sin }^4\theta )$is

$\frac{y-4{\sin }^4\theta }{x-4{\cos }^4\theta }=-{\tan }^2\theta$

$\Rightarrow x$ intercept $=4{\cos }^2\theta$

$\Rightarrow y$ intercept $=4{\sin }^2\theta$

So, the sum of intercept made on the coordinate axes $=4({\sin }^2\theta +{\cos }^2\theta )=4$