Find the required point be `P(x_1, y_1)dot` The tangent to the curve `sqrt(x)+sqrt(y)=4` at which tangent is equally inclined to the axes.

Answer

The required points are `(4,4)`.

Explanation

ATQ,
$$
\begin{aligned}
&\sqrt{x}+\sqrt{y}=4 \\
&\Rightarrow x^{\frac{1}{2}}+y^{\frac{1}{2}}=4 \\
&\Rightarrow \frac{1}{2} \cdot \frac{1}{x^{\frac{1}{2}}}+\frac{1}{2} \cdot \frac{1}{y^{\frac{1}{2}}} \cdot \frac{d y}{d x}=0 \\
&\therefore \frac{d y}{d x}=-\frac{1}{2} \cdot x^{-\frac{1}{2}} 2 \cdot y^{\frac{1}{2}} \\
&=-\sqrt{\frac{y}{x}}
...