Hi I'm stucked with this equation while transforming it into circle equation:
equation is
$y+\sqrt{x-x^2} = 0$
Here is my solution: $$y+\sqrt{x-x^2} = 0$$ $$y+\sqrt{-1(x^2-x)} = 0$$ $$y+\sqrt{-1\left(\left(x-\frac 12\right)^2-\frac 14\right)} = 0\qquad (\ )^2$$ $$y^2-\left(x-\frac 12\right)^2+\frac14 = 0\qquad\quad\ \ \frac{-1}4$$ $$y^2-\left(x-\frac 12\right)^2 = \frac{-1}4\qquad\qquad\times(-1)$$ $$\left(x-\frac{ 1}2\right)^2 - y^2 = \frac 14$$
According to Wolframalpha original equation is half-circle with middle in $\left[\dfrac 12,0\right]$ with radius $\dfrac12$ (http://www.wolframalpha.com/input/?i=y+%2B+sqrt%28x-x%5E2%29+%3D+0) but my solution is draw as parabola (http://www.wolframalpha.com/input/?i=%28x-1%2F2%29%5E2-%28y%5E2%29+%3D+1%2F4). What am I doing wrong?
Thanks
HINT: $y$ on the other side, then square both sides. Your solution is incorrect, because $(a+b)^2\neq a^2+b^2$.