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Geometry · Chapter 10 · Lesson 10.16 · Printable PDF

Finding the Center and Radius Worksheet with Answer Key

6 problems on finding a circle's center and radius by completing the square, with equations not in standard shape, a student's error, a security light, and circles crossing the axes. 2 pages, with a worked answer key.

6 problems2 pagesanswer key
Printable Finding the center and radius worksheet with answer key - Geometry (Page 1 PDF preview)
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What's on the worksheet

  1. Complete the square to write each circle in standard form and give its center and radius.
    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. Rearrange and divide first, then complete the squares to find the center and radius.
    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. Find Priya's mistake in completing the square and correct it.
  4. Find the center and radius of the lit patch and where it meets the fence.
  5. Decide whether each circle crosses, touches or misses each axis and give the points.
  6. Show with letters that an equation with a negative constant term is a circle.

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The free lesson teaches it with worked examples and practice problems.

Finding the center and radius: the lesson ›

More Chapter 10 worksheets: Circles