Question: 10. Write the standard form of the circle. a. $(x - 4)^2 + (y - 4)^2 = 9$ b. $(x - 4)^2 + (y - 4)^2 = 3$ c. $(x + 4)^2 + (y + 4)^2 = 3$ d. $(x + 4)^2 + (y + 4)^2 = 9$ 11. List the intercepts of the graph. a. $(0, -\frac{\pi}{2}), (0, -4), (0, \frac{\pi}{2})$ b. $(-\frac{\pi}{2}, 0), (-4, 0), (\frac{\pi}{2}, 0)$ c. $(0, -\frac{\pi}{2}), (-4, 0), (0, \frac{\pi}{2})$ d. $(-\frac{\pi}{2}, 0), (0, -4), (\frac{\pi}{2}, 0)$ 12. Find the slope and y-intercept of the line and graph it. $x + 2y = 6$ 13. Graph the line containing the point $P$ and having slope $m$. $P = (-2, 8); m = 0$ 14. List the intercepts of the graph. Tell whether the graph is symmetric with respect to the x-axis, y-axis, origin, or none of these. 15. Find the center $(h, k)$ and radius $r$ of the circle. Graph the circle. $(x - 5)^2 + (y - 1)^2 = 3$

1. **Problem 10:** Write the standard form of the circle. The standard form of a circle is given by: $$ (x - h)^2 + (y - k)^2 = r^2 $$ where $(h, k)$ is the center and $r$ is the radius. - a. $(x - 4)^2 + (y - 4)^2 = 9$ has center $(4,4)$ and radius $r = \sqrt{9} = 3$. - b. $(x - 4)^2 + (y - 4)^2 = 3$ has center $(4,4)$ and radius $r = \sqrt{3}$. - c. $(x + 4)^2 + (y + 4)^2 = 3$ has center $(-4,-4)$ and radius $r = \sqrt{3}$. - d. $(x + 4)^2 + (y + 4)^2 = 9$ has center $(-4,-4)$ and radius $r = 3$. 2. **Problem 11:** List the intercepts of the graph. - a. $(0, -\frac{\pi}{2}), (0, -4), (0, \frac{\pi}{2})$ are all y-intercepts. - b. $(-\frac{\pi}{2}, 0), (-4, 0), (\frac{\pi}{2}, 0)$ are all x-intercepts. - c. $(0, -\frac{\pi}{2}), (-4, 0), (0, \frac{\pi}{2})$ mix of x and y intercepts. - d. $(-\frac{\pi}{2}, 0), (0, -4), (\frac{\pi}{2}, 0)$ mix of x and y intercepts. 3. **Problem 12:** Find the slope and y-intercept of the line $x + 2y = 6$. Rewrite in slope-intercept form $y = mx + b$: $$ x + 2y = 6 $$ $$ 2y = 6 - x $$ $$ y = \frac{6 - x}{2} = 3 - \frac{1}{2}x $$ So slope $m = -\frac{1}{2}$ and y-intercept $b = 3$. 4. **Problem 13:** Graph the line containing point $P = (-2, 8)$ with slope $m = 0$. A slope of zero means a horizontal line passing through $y = 8$. Equation: $$ y = 8 $$ 5. **Problem 14:** List the intercepts of the graph and symmetry. (Since no specific graph equation is given, this is a general instruction.) 6. **Problem 15:** Find the center and radius of the circle: $$ (x - 5)^2 + (y - 1)^2 = 3 $$ Center $(h, k) = (5, 1)$. Radius: $$ r = \sqrt{3} $$ **Summary:** - Problem 10: Standard form and radius from given options. - Problem 11: Identify intercepts. - Problem 12: Slope $m = -\frac{1}{2}$, y-intercept $3$. - Problem 13: Horizontal line $y=8$. - Problem 15: Circle center $(5,1)$, radius $\sqrt{3}$.