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Equation of A Circle

Equation of A Circle. Keystone Geometry Unit 7. Equation of a Circle. The center of a circle is given by (h, k ). The radius of a circle is given by r. The equation of a circle in standard form is: (x – h) 2 + (y – k) 2 = r 2. Finding the Equation of a Circle . Circle O

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Equation of A Circle

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  1. Equation of A Circle Keystone Geometry Unit 7

  2. Equation of a Circle The center of a circle is given by (h, k). The radius of a circle is given by r. The equation of a circle in standard form is: (x – h)2 + (y – k)2 = r2

  3. Finding the Equation of a Circle Circle O The center is (0, 0) so it is located at the origin. The radius is 12. The equation is x 2 + y 2 = 144

  4. Finding the Equation of a Circle Circle A The center is (16, 10) The radius is 10 The equation is (x – 16)2 + (y – 10)2 = 100 Circle B The center is (4, 20) The radius is 10 The equation is (x – 4)2 + (y – 20)2 = 100

  5. Graphing Circles (x – 3)2 + (y – 2)2 = 9 Center (3, 2) Radius of 3

  6. Graphing Circles (x + 4)2 + (y – 1)2 = 25 Center (-4, 1) Radius of 5

  7. Graphing Circles (x – 5)2 + y2 = 36 Center (5, 0) Radius of 6

  8. Writing Equations of Circles Write the standard equation of the circle with a center at (4, 7) and a radius of 5. (x – 4)2 + (y – 7)2 = 25 Write the standard equation of the circle with a center at (-3, 8) and a radius of 6.2 (x + 3)2 + (y – 8)2 = 38.44

  9. Writing Equations of Circles Write the standard equation of the circlewith a center at (2, -9) and a radius of . (x – 2)2 + (y + 9)2 = 11 Write the standard equation of the circle with a center at (0, 6) and a radius of . x 2 + (y – 6)2 = 7

  10. Writing Equations of Circles Write the standard equation of the circle with a center at (-1.9, 8.7) and a radius of 3. (x + 1.9)2 + (y – 8.7)2 = 9

  11. -7 -2 -1 1 3 5 7 -6 -5 -4 -3 0 4 6 8 2 Identify the center and radius and sketch the graph: Remember, the center values end up being the opposite sign of what is with the x and y and the right hand side is the radius squared. So the center is at (-4,3) and the radius is 5.

  12. But what if the equation of a circle is not in standard form but multiplied out (FOILED)! Moving everything to one side in descending order and combining like terms we’d have: If we'd have started with it like this, we'd have to complete the square on both the x's and y's to get in standard form.

  13. Move constant to the other side Group x terms and a place to complete the square Group y terms and a place to complete the square 4 16 4 16 Complete the square, write factored form, and we would be back to the standard form for the equation of a circle with a center at (-2,4) and a radius of 2.

  14. Writing a Standard Equation of a Circle • The point (1, 2) is on a circle whose center is (5, -1). Write a standard equation of the circle. • First solve for the radius: • Then plug h, k and r in to the standard equation of a circle:

  15. Another example: Find the center, the length of the radius, and write the equation of the circle if the endpoints of a diameter are (-8,2) and (2,0). Center: Use midpoint formula! Length: use distance formula with radius and an endpoint Equation: Put it all together

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