c o n i c s e c t i o n s part 2: the circle. circle ellipse (x-h) 2 +(y-k) 2 =r 2 ellipse x &...
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![Page 1: C O N I C S E C T I O N S Part 2: The Circle. Circle Ellipse (x-h) 2 +(y-k) 2 =r 2 Ellipse x & yPoints on the circle. h & kThe center of the circle. rThe](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649dbf5503460f94ab333d/html5/thumbnails/1.jpg)
C O N I CS E C T I O N S
Part 2: The Circle
![Page 2: C O N I C S E C T I O N S Part 2: The Circle. Circle Ellipse (x-h) 2 +(y-k) 2 =r 2 Ellipse x & yPoints on the circle. h & kThe center of the circle. rThe](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649dbf5503460f94ab333d/html5/thumbnails/2.jpg)
Circle
Ellipse
(x-h)2+(y-k)2=r2
Ellipsex & y Points on the circle.
h & k The center of the circle.
r The radius of the circle.
Example: (x+1)2 + (y–3)2 = 20 Center location: ( -1 , 3 )( h , k )
Radius: 2 √5 units
Diameter: 4 √5 units
![Page 3: C O N I C S E C T I O N S Part 2: The Circle. Circle Ellipse (x-h) 2 +(y-k) 2 =r 2 Ellipse x & yPoints on the circle. h & kThe center of the circle. rThe](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649dbf5503460f94ab333d/html5/thumbnails/3.jpg)
Example: (x – 4)2 + (y + 2)2 = 16
4 units
(4, –2)Center location:
Radius:
Let’s Graph a Circle!!!
![Page 4: C O N I C S E C T I O N S Part 2: The Circle. Circle Ellipse (x-h) 2 +(y-k) 2 =r 2 Ellipse x & yPoints on the circle. h & kThe center of the circle. rThe](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649dbf5503460f94ab333d/html5/thumbnails/4.jpg)
You can’t fool us. It’s not that easy!
![Page 5: C O N I C S E C T I O N S Part 2: The Circle. Circle Ellipse (x-h) 2 +(y-k) 2 =r 2 Ellipse x & yPoints on the circle. h & kThe center of the circle. rThe](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649dbf5503460f94ab333d/html5/thumbnails/5.jpg)
(x – h)2 + (y – k)2 = r2
Write the equation of the circle with endpoints (diameter) of (7, –3) and (5, 5)
x1 x2
2,y1 y2
2
7 5
2, 35
2
Center: (6, 1)
Use the distance formula to find the radius…
d x1 x2 2 y1 y2 2
(x – 6)2 + (y – 1)2 = 17
22 5156 17
The center of the circle is the midpoint of the endpoints (diameter).
Radius:
→
![Page 6: C O N I C S E C T I O N S Part 2: The Circle. Circle Ellipse (x-h) 2 +(y-k) 2 =r 2 Ellipse x & yPoints on the circle. h & kThe center of the circle. rThe](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649dbf5503460f94ab333d/html5/thumbnails/6.jpg)
Hang on!
You said that we needed completing the square for Conic Sections!
![Page 7: C O N I C S E C T I O N S Part 2: The Circle. Circle Ellipse (x-h) 2 +(y-k) 2 =r 2 Ellipse x & yPoints on the circle. h & kThe center of the circle. rThe](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649dbf5503460f94ab333d/html5/thumbnails/7.jpg)
What is the equation and graph of the circle: x2 + 8x + y2 – 6y – 11 = 0
x2 + 8x + y2 – 6y = 11+ 16
(x + 4)2 + (y – 3)2 = 36
Radius = 6
Center (–4, 3)
+ 9
(8 / 2)2 = 16
+ 16 + 9
(-6 / 2)2 = 9
![Page 8: C O N I C S E C T I O N S Part 2: The Circle. Circle Ellipse (x-h) 2 +(y-k) 2 =r 2 Ellipse x & yPoints on the circle. h & kThe center of the circle. rThe](https://reader035.vdocuments.mx/reader035/viewer/2022062407/56649dbf5503460f94ab333d/html5/thumbnails/8.jpg)
I like circles!