Test Your Knowledge: Graphing Circles from Their Standard Equation

📚 Quick Study Guide

• 📐 The standard equation of a circle is: $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius.
• 🧭 To find the center, identify $h$ and $k$ from the equation. Remember to take the opposite sign of the numbers inside the parentheses!
• 📏 To find the radius, take the square root of the number on the right side of the equation: $r = \sqrt{r^2}$.
• ✍️ Once you have the center and radius, you can graph the circle by plotting the center and then marking points $r$ units away in all four directions (up, down, left, and right).
• 💡 If the equation is not in standard form, you may need to complete the square to rewrite it.

Practice Quiz

1. What is the center of the circle given by the equation $(x - 3)^2 + (y + 2)^2 = 16$?

   1. (3, 2)
   2. (-3, -2)
   3. (3, -2)
   4. (-3, 2)

2. What is the radius of the circle given by the equation $(x + 1)^2 + (y - 4)^2 = 25$?

   1. 5
   2. 25
   3. -5
   4. 625

3. What is the equation of a circle with center at (0, 0) and radius 7?

   1. $x^2 + y^2 = 49$
   2. $x^2 + y^2 = 7$
   3. $(x - 7)^2 + (y - 7)^2 = 0$
   4. $(x + 7)^2 + (y + 7)^2 = 0$

4. What is the equation of a circle with center at (-2, 1) and radius 3?

   1. $(x - 2)^2 + (y + 1)^2 = 9$
   2. $(x + 2)^2 + (y - 1)^2 = 9$
   3. $(x - 2)^2 + (y + 1)^2 = 3$
   4. $(x + 2)^2 + (y - 1)^2 = 3$

5. The equation $(x - 5)^2 + y^2 = 4$ represents a circle. What is its center?

   1. (5, 0)
   2. (0, 5)
   3. (-5, 0)
   4. (0, -5)

6. What is the radius of the circle defined by the equation $x^2 + (y + 3)^2 = 1$?

   1. 1
   2. -1
   3. 3
   4. 9

7. A circle has center (4, -6) and radius 8. Which of the following is its equation?

   1. $(x - 4)^2 + (y + 6)^2 = 64$
   2. $(x + 4)^2 + (y - 6)^2 = 64$
   3. $(x - 4)^2 + (y + 6)^2 = 8$
   4. $(x + 4)^2 + (y - 6)^2 = 8$