Finding the Center and Radius Worksheet with Answer Key

What's on the worksheet

1. Complete the square in x and in y to write each circle in standard form.
   x^2 + y^2 - 6x + 10y + 18 = 0x^2 + y^2 + 12x - 13 = 0x^2 + y^2 + 2x + 14y + 25 = 0x^2 + y^2 - 8x - 4y + 11 = 0x^2 + y^2 + 10x - 6y + 22 = 0
2. Each equation is a circle, but not yet in the shape x² + y² + Dx + Ey + F = 0.
   2x^2 + 2y^2 - 12x + 8y - 24 = 0x^2 + y^2 + 5x + y - \dfrac{1}{2} = 0x^2 + 8y = 9 - y^2 + 6x9x^2 + 9y^2 + 18x - 12y - 23 = 0x(x - 4) + y(y + 6) = 12
3. Priya was asked for the center and radius of x² + y² + 8x - 2y - 8 = 0.
4. A security light on a pole lights a round patch of a yard.
5. For each circle, decide whether it crosses, touches or misses the x-axis, and the same for the y-axis.
6. An equation x² + y² + Dx + Ey + F = 0 has a negative constant term, F < 0.