Equation of a Circle Worksheet with Answer Key

What's on the worksheet

1. Write the equation of each circle in standard form.
   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 the radius of each circle.
   (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. On a garden plan marked in meters, the edge of a round flower bed is the circle (x + 4)² + (y - 4)² = 5.
4. On a garden plan marked in meters, a sprinkler stands at (3, −2).
5. A circle touches the x axis at exactly one point when the distance from its center to the x axis equals its radius, and likewise for the y axis.
6. A student was asked for the equation of the circle with center (−3, 5) and radius 4, and wrote (x - 3)² + (y + 5)² = 4.
7. A circle has its center on the x axis and passes through the points A(1, 3) and B(5, 1).
8. On a workshop plan, the edge of a round post is the circle (x + 1)² + (y - 2)² = 10.