1.5Circles.notebook
September 15, 2015
9/15/15
Do Now
Solve each equation below by factoring.
1. k2 +6k =­5
2. x2 ­ 24= 2x
Solve each equation below by completing the square.
1. n2 ­12n ­25= 3
2. n2 ­ 14n­ 35= ­3
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1.5Circles.notebook
September 15, 2015
Solve each equation below by completing the square.
1. b2 +20b +82= ­9
2. n2 ­ 10n­ 75= ­7
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1.5Circles.notebook
September 15, 2015
Section 1.5: Circles
Learning Target: Properties of a Circle
Success Criteria: I will be able to find the equation of a circle and graph a circle.
Standard Form of an Equation of a Circle:
(x­ h)2 + (y­ k)2 = r2
r = radius
(h,k)= Center of Circle
Ex: Write the equation of the circle with radius 7 and center (3, ­2).
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1.5Circles.notebook
September 15, 2015
Write the equation of the circle in standard form if the radius is 11 and the center is (­6, 5).
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1.5Circles.notebook
September 15, 2015
Graph the equation: (x + 2)2 + (y ­ 1)2 = 25
Center = (h,k) = (­2,1)
h
k
y
r = √25 = 5
Plot the center, then move up 5 and plot a point, move down from the center 5, then left from the center 5 and right from the center 5 to get the edges of the circle and then draw that best most accurate circle that you can draw., down, left, and right
r2
(­2,6)
x (­7,1)
(­2,1)
(3,1)
(­2,­4)
Make sure you label points.
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1.5Circles.notebook
September 15, 2015
Graph the equation: (x ­4)2 + (y­ 6)2 = 9 6
1.5Circles.notebook
September 15, 2015
General Form of the Equation of a Circle:
x2 + y2 + ax + by + c = 0
expanded form of standard form
Example: Find the center and the radius for the equation below.
x2 + y2 + 4x ­6y +12 =0.
1. Group all the x's, y's together and move the constant to the other side.
2. Complete the square for each part.
3. Factor the x's and the y's and rewrite into standard form.
x2 + y2 + 4x ­6y +12 =0.
Example:
Step 1:
(x2 + 4x) + (y2 ­6y)= ­12
Step 2: In order to complete the square we take b 2
the b coefficient and find ( )
2
(x2 + 4x+ __) + (y2 ­6y+__ )= ­12+ __ + __
a
b
c
a
b
c
What we add to one side we must add to other side of equals sign
2
2
(6 )
2 ­6y+__ )= ( 42 )
(6 )
( 42 )
(x2 + 4x+ __ ) + (y
­12+ __ + __
2
2
2
2
Step 3
(x2 + 4x+ 4) + (y2 ­6y+ 9)= ­12+ 4 + 9
Now we factor these parts
(x + 2)(x+2) + (y ­3)(y­ 3) = 1
Which we can rewrite as: (x+ 2)2 + (y­ 3)2 = 1
k
r2
h Center = (h,k)= (­2, 3) radius= r = √ 1 = 1
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1.5Circles.notebook
September 15, 2015
Section 1.5 Pg. 50
#7­15, 21­29, 31, 35­39, 47
all odds
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1.5Circles.notebook
September 15, 2015
Find the general equation of the circle whose center is (1,­2) and whose graph contains the point (4,­2).
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