warm up. what is the area & circumference of a circle?
TRANSCRIPT
![Page 1: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/1.jpg)
Warm Up
![Page 2: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/2.jpg)
Area & Equation of Circles
May 1st, 2014
![Page 3: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/3.jpg)
![Page 4: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/4.jpg)
What is the area & circumference of a circle?
rC
rA
2
2
![Page 5: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/5.jpg)
Review• Find the area of a circle with r =5
• Find the area of a circle with r = √2
• If the area of a circle is 81𝝅 what is the radius?
![Page 6: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/6.jpg)
Example• Lance decides he would like the
garden to have a circumference of 40π feet. What would be the area of this garden?
![Page 7: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/7.jpg)
ExampleLance is also considering including a
sidewalk around the outside of the garden, as shown below. Determine the area of the sidewalk.
![Page 8: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/8.jpg)
![Page 9: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/9.jpg)
X & Y and H & KA circle is the set of all points in a plane that are equidistant from a given point called the center.
![Page 10: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/10.jpg)
The Equation of a Circle Derived from Pythagorean Theorem
![Page 11: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/11.jpg)
EQUATION OF A CIRCLE
![Page 12: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/12.jpg)
Write the equation of the circle described …• Center (0, 3) and radius = 5
• Center (-1, 5) and radius = 7
![Page 13: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/13.jpg)
Write the equation of the circle….
![Page 14: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/14.jpg)
Write the equation of the circle…
• Center (2, -1) and contains the point (0, 4)
![Page 15: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/15.jpg)
Write the equation of a circle• Endpoints of the diameter (-1,
3) and (5, 1)
![Page 16: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/16.jpg)
Identify the center and radius of the circle…• (x – 3)2 + (y + 1)2 = 49
• x2 + (y – 5)2 = 10
![Page 17: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/17.jpg)
Systems with Circles and Linear Equations
![Page 18: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/18.jpg)
How do we solve algebraically?• We take the linear equation
(solve for y) and plug into the circle
![Page 19: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/19.jpg)
Let’s try one!• Solve by graphing…
![Page 20: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/20.jpg)
Now solve algebraically!• Step 1: Get “y” by itself• Step 2: Substitute linear equation in for “y” in the
circle• Step 3: Multiply out & simplify• Step 4: Factor• Step 5: Plug in x values to get y values
![Page 21: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/21.jpg)
Solve the system by graphing:
![Page 22: Warm Up. What is the area & circumference of a circle?](https://reader036.vdocument.in/reader036/viewer/2022081511/56649ef95503460f94c0b531/html5/thumbnails/22.jpg)
Homework
• Worksheet