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C O N I CS E C T I O N S
Part 2: The Circle
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
Example: (x – 4)2 + (y + 2)2 = 16
4 units
(4, –2)Center location:
Radius:
Let’s Graph a Circle!!!
You can’t fool us. It’s not that easy!
(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:
→
Hang on!
You said that we needed completing the square for Conic Sections!
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
I like circles!