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

2. Circle Ellipse (x-h) 2 +(y-k) 2 =r 2 Ellipse x & yPoints on the circle. h & kThe center of the circle. rThe 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

3. Example: (x – 4) 2 + (y + 2) 2 = 16 4 units (4, –2)Center location: Radius: Let’s Graph a Circle!!!

4. You can’t fool us. It’s not that easy!

5. (x – h) 2 + (y – k) 2 = r 2 Write the equation of the circle with endpoints (diameter) of (7, –3) and (5, 5) Center: (6, 1) Use the distance formula to find the radius… (x – 6) 2 + (y – 1) 2 = 17 The center of the circle is the midpoint of the endpoints (diameter). Radius: →

6. Hang on! You said that we needed completing the square for Conic Sections!

7. What is the equation and graph of the circle: x 2 + 8x + y 2 – 6y – 11 = 0 x 2 + 8x + y 2 – 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

8. I like circles!