Consider the curve C given by the following equation $$ \sqrt{x}+\sqrt{y}=\sqrt{a} $$ where $a$ is a constant with the condition $a > 0$.
Let $(x_0, y_0)$ with be a point on C such that $x>0$ and $y>0$. Now, assume that $(x_1, 0)$ and $(0, y_1)$ be considered $x$ and $y$ such that intercepts of the tangent line to C at $(x_0, y_0)$.
My question: How to proof that $x_1 + y_1 = a$?
My try:
Currently I just found the derivative using implicit differentiation, and used the slope for its tangent line, but now I'm lost and not sure what to don.
Thanks for any suggestion.