1. April 20, 2012 Conic Sections - Circles
Warm-up:
In partners, do parabola construction.
I will go around and check your homework.
Quiz Mon/Tues!
HW 8.3 Pg. 429 #8, 9, 16-20

2. Correct HW 8.2 Pg. 423 #5, 6, 22, 23, 25

3. Standard form of a circle is:
Lesson 8.3 Circles
Standard form of a circle is:
(x – h)2 + (y – k)2 = r2
Center: (h, k)
Radius: r
Example 1: Identify the center and radius of the circle: (x – 3)2 + (y + 4)2 = 25
Center (3, -4) and radius = 5

4. Now sketch the circle: (x – 3)2 + (y + 4)2 = 2510 -5
-10 5
Center: (3, -4)
Radius: 5
You try: Identify the center, radius and sketch the circle:
(x + 2)2 + y2 = 36

5. Standard form of a circle is: (x – h)2 + (y – k)2 = r2 Center: (h, k) Radius: r
Example 2:
A certain wireless transmitter has a range of 30 miles in any direction. If a Wi-Fi phone is 4 miles south and 3 miles west of headquarters, write an equation to represent the area within which the phone can operate via the Wi-Fi system.
Identify the center:
Identify the radius:

6. Practice
Write an equation for the circle that has a center at (4, 0) and radius of 4 and sketch.
The radar for a county airport control tower is located at (5, 10) on a map. It can detect a plane up to 20 miles away. Write an equation for the outer limits of the detection area.

7. What if it is not given in Standard Form??? (x – h)2 + (y – k)2 = r2
Example 3: x2 + y2 – 4x + 8y – 5 = 0
1. Rewrite so that x and y terms are grouped together. 4 16 +4
+16
2. Then put the constant on other side of the equation
Center: (2, -4)
Radius: r = 5
3. Use completing the square.
4. Make sure to add the number to the other side of the equation too!

8. Aliens or great mathematicians?

9. Review for Monday’s Quiz
Find the center and the radius of
x2 + (y – 3)2 = 100, sketch.
Rewrite the equation in standard form, then identify all parts of the parabola
y = x2 – 8 – 11
3. Distance and Midpoint Formulas