Equation of a Circle Worksheet with Answer Key

What's on the worksheet

1. Write the equation of each circle in standard form from its center and radius.
   center (−8, 0), r = 5center \left(\dfrac{1}{2}, -4\right), r = 3center (−3, −9), r = 2\sqrt{5}center (0, −6), r = \dfrac{3}{4}center (11, 4), d = 14
2. Find the center and exact radius of each circle from its equation.
   (x - 4)^2 + (y + 11)^2 = 81x^2 + (y - 3)^2 = 45(x + 7)^2 + (y + 7)^2 = 505(x + 1)^2 + 5(y - 6)^2 = 80\left(x - \dfrac{3}{2}\right)^2 + y^2 = \dfrac{49}{4}
3. Write the equation of the outer edge of a gravel path around a round flower bed.
4. Write the equation and an inequality for the ground a sprinkler waters.
5. Write the equation of circles that touch both axes.
6. Name the two mistakes in a student's circle equation and write the correct one.
7. Find the center and equation of a circle with its center on the x axis through two points.
8. Find where a rope on a line meets a round post and decide whether it cuts across.