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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