Aim #9: How do we write the equation of a circle



Aim #9e: How do we write the equation of a circle/find its center & radius?

Do Now:

Graph the points: (1,-1) , (-3,-1) , & (-6,2)

Construct the point that is

equidistant from all 3 points :

Which of the four centers does this

point represent?

Draw the path of equidistance.

Write the equation.

{Hint: What 2 important pieces of information

that remain fixed will we need to write such

an equation? What changes?}

Which formula/equation can we use to find the length of the _____________ of the circle?

_____________________________________________________

1) What could we do to simplify this equation?

Now we can make some substitutions:

2) Let [pic], the radius 3) [pic] simplifies to [pic]

4) [pic] is the center and swaps out for [pic]

________________________________ is the center-radius form of the equation of a circle where (h, k) is the center and “ r ” is the radius

For each circle : Fill in the missing information: For 13-16, write the equation.

| |Center |Radius |Equation |

|1. |(0, 0) |r = 3 | |

|2. |(0, 0) |r = 8 | |

|3. |(5, 3) |r = 7 | |

|4. |(-1, 2) |r = 9 | |

|5. |(8, -9) |[pic] | |

|6. |(-7, -3) |[pic] | |

|7. | | |[pic] |

|8. | | |[pic] |

|9. | | |[pic] |

|10. | | |[pic] |

|11. | | |[pic] |

|12. | | |[pic] |

Name ________________________________ Hw #______ pd _____ #______

For questions 1 & 2, find the center and radius, then graph each circle.

Use the information provided to write the equation of each circle.

3) Center: (13,-13) 4) Center: (13,-13)

Radius: 4 Point on Circle: (-10,-16)

5) Endpoints of diameter: 6) Center: (0, 13)

(18,-13) and (4,-3) [pic]

7) center is (3,5) 8) Endpoints of the diameter are

point on the circle is (-6,4) (-7,5) & (3,5)

(on circumference)

9) Construct the point that is

equidistant from: (1,5) , (4,2) , & (0,2)

Which of the four centers does this

point represent?

Draw the path of equidistance.

Write the equation.

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