potting of fractional exponential graph

Question

Sir, please tell me how to draw the graph of $x^{1/2} + y^{1/2} = a^{1/2}$?

I tried it many a times but couldn't find the solution. Please help me in solving the problem.

Answer 1

$$ y=(\sqrt a - \sqrt x)^2=x-2\sqrt{ax}+a, $$ and of course $x\ge0$, $y\ge0$, $a\ge0$.

Answer 2

This is a parabola that exists in the first quadrant only. It has intercept = a = 1 on x and y axes. The parabola touches x- and y- axes at (1,0) and (0,1).

There is no graph beyond the small arc seen here.

It can be graphed on WA for example. It has parametric form $ (x/a = \cos^{4} \theta,y/a = \sin^{4} \theta); \sqrt {x/a} + \sqrt {y/a} =1. $