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C O N I C S E C T I O N S Part 2: The Circle

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

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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

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

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

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

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

(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

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

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

I like circles!