circles unit 3-2. equations we’ll need: distance formula midpoint formula
TRANSCRIPT
![Page 1: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/1.jpg)
CIRCLES
Unit 3-2
![Page 2: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/2.jpg)
Equations we’ll need:
Distance formula
Midpoint formula
2 2
1 2 1 2d x x y y
1 2 1 2( , ) ,2 2
x x y yM x y
![Page 3: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/3.jpg)
Definitions
Circle: Set of all points in a plane that is a fixed distance from a fixed point
Center: The fixed equidistance point of the circle
Radius: The fixed equidistance length of the circle
![Page 4: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/4.jpg)
Circle Equation
2 2 2( ) ( )x h y k r
( , )Center h k
Radius r
![Page 5: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/5.jpg)
Example 1
Name the center and the radius of this circle,
and graph it2 2( 2) ( 3) 16x y
2 2 2( ) ( )x h y k r ( 2,3)
4
c
r
2 16
4
r
r
![Page 6: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/6.jpg)
Example 1
Name the center and the radius of this circle, and graph it
2 2 2( 2) ( 3) 4x y
2 2( 2) ( 3) 16x y
( 2,3)
4
c
r
![Page 7: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/7.jpg)
Example 2Write an equation of the circle with its center at
(–3, 5), the radius is 5 and graph it.
2 2 2( ) ( )x h y k r
![Page 8: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/8.jpg)
Example 3Name the center and the radius of this circle,
and graph it
2 2 2( ) ( )x h y k r
2 2 25x y
![Page 9: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/9.jpg)
YOUR TURN!Graph the equation 2 2( 3) ( 2) 9x y
![Page 10: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/10.jpg)
2.3 - Circles 1004/18/23 19:36
Example 4
Find the radius, graph the circle, and write the equation in standard form with the given center of (2, -3) and the point (1, 0).
2 2 2( ) ( )x h y k r
C
radius
2 2
1 2 1 2d x x y y
2 22 1 3 0d
2 21 3d
1 9 10d radius
![Page 11: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/11.jpg)
2.3 - Circles 1104/18/23 19:36
Example 4
Find the radius, graph the circle, and write the equation in standard form with the given center of (2, -3) and the point (1, 0).
2 2 2( ) ( )x h y k r
C
radius =
10
10
(2, 3)
r
C
22 2( 2) ( ( 3)) 10x y
2 2( 2) ( 3) 10x y
![Page 12: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/12.jpg)
2.3 - Circles 1204/18/23 19:36
Write a circle equation whose center is at the origin and passes through (1, –6).
2 2 2( ) ( )x h y k r Example 5
![Page 13: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/13.jpg)
2.3 - Circles 1304/18/23 19:36
Write a circle equation whose center is at (1, 0) and passes through (-2, 3)
2 2 2( ) ( )x h y k r YOUR TURN!
![Page 14: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/14.jpg)
2.3 - Circles 1404/18/23 19:36
Write a circle equation whose endpoints of a diameter are (-5, 2) and (3, 6).
1 2 1 2,2 2
x x y yMP
2 2 2( ) ( )x h y k r Example 6
Diameter
5 3 2 6,
2 2MP
1,4MP Center
![Page 15: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/15.jpg)
2.3 - Circles 1504/18/23 19:36
Write a circle equation whose endpoints of a diameter are (-5, 2) and (3, 6).
2 2 2( ) ( )x h y k r Example 6
2 2
1 2 1 2d x x y y
1,4MP Center
Center
Radius
2 25 ( 1) 2 4d
2 24 2d
16 4 20d Radius
![Page 16: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/16.jpg)
2.3 - Circles 1604/18/23 19:36
Write a circle equation whose endpoints of a diameter are (-5, 2) and (3, 6).
2 2 2( ) ( )x h y k r Example 6
20
( 1,4)
r
C
2 2( 1) ( 4) 20x y
22 2( ( 1)) ( 4) 20x y
![Page 17: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/17.jpg)
2.3 - Circles 1704/18/23 19:36
YOUR TURN!
Write a circle equation whose endpoints of a diameter are (5, 4) and (-1, -6).
1 2 1 2,2 2
x x y yMP
2 2 2( ) ( )x h y k r
2 2
1 2 1 2d x x y y
![Page 18: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/18.jpg)
2.3 - Circles 1804/18/23 19:36
Determine the equation of this circle by the graph given
Example 7
![Page 19: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/19.jpg)
2.3 - Circles 1904/18/23 19:36
YOUR TURN!
Determine the equation of this circle by the graph given
![Page 20: CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula](https://reader031.vdocuments.site/reader031/viewer/2022032201/56649d1b5503460f949f0f44/html5/thumbnails/20.jpg)
2.3 - Circles 2004/18/23 19:36
Assignment
WORKSHEET!