Question

The point on the curve $\sqrt{x}+\sqrt{y}=2a^2$, where the tangent is equally inclined to the axes, is

• A. $(a^4,a^4)$
• B. $(0,4a^4)$
• C. $(4a^4,0)$
• D. none of these

Answer 1

The correct option is A $(a^4,a^4)$

$y=x$ is the equation of line as it is equally inclined to axes
So let point $(k,k)$ is the point of tangency
Therefore, $\sqrt{k}+\sqrt{k}=2a^{2}k=a^4$
Hence point is $(a^4,a^4)$