Semicircle - Sketching Points

Question

I am having problems understanding how to sketch/solve $x = \sqrt{1 - (y-1)^2}$.

Please, any help is much appreciated.

Answer 1

$x=\sqrt{1-(y-1)^2}$

$x^2=1-(y-1)^2$

$(y-1)^2=1-x^2$

$(y-1)=\sqrt{1-x^2}$

$y=\sqrt{1-x^2}+1$

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Note that since the original equation yields $x\geq0$, only the right side of the graph below is relevant:

Answer 2

Square both sides and simplify to get the equation of a well known curve. Then, note that $x \gt 0$

Answer 3

Hint:

$$(x-a)^{2}+(y-b)^{2}=r^{2}$$

is the equation of a circle with radius $r$ and center at $(a,b)$. In your case, x is restricted to

$$0\leq x \leq a+r$$