Question

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

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

Explanation:

Step1: Start with circle equation

\((x - h)^2+(y - k)^2=r^2\)

Step2: Isolate \((x - h)^2\)

\((x - h)^2=r^2-(y - k)^2\)

Step3: Take square - root of both sides

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

Step4: Solve for \(h\)

\(h=x\pm\sqrt{r^2-(y - k)^2}\), considering the form of the options, we take \(h = x-\sqrt{r^2-(y - k)^2}\)

Answer:

\(h=x-\sqrt{r^2-(y - k)^2}\) (corresponding to the first option in the image where the correct form for solving for \(h\) from the circle equation \((x - h)^2+(y - k)^2=r^2\) is presented in the way of isolating \(h\) and taking the negative square - root case as per the options)