Question

1. the standard equation of a circle is (x - h)^2+(y - k)^2 = r^2. rearrange the equation for h.

o h = r^2-(y - k)^2 - x
o h = -\sqrt{r^2-(y - k)^2}+x
o h = \sqrt{r^2-(y - k)^2}-x
o h = \sqrt{r^2-(y - k)^2 - x}

Explanation:

Step1: Isolate $(x - h)^2$

$(x - h)^2=r^{2}-(y - k)^2$

Step2: Take square - root of both sides

$x - h=\pm\sqrt{r^{2}-(y - k)^2}$

Step3: Solve for $h$

$h=x\mp\sqrt{r^{2}-(y - k)^2}$

Answer:

$h = x-\sqrt{r^{2}-(y - k)^2}$ or $h = x+\sqrt{r^{2}-(y - k)^2}$ (The closest option from the given ones is $h=-\sqrt{r^{2}-(y - k)^2}+x$) so the answer is $h = -\sqrt{r^{2}-(y - k)^2}+x$