Circles: parts and equations

Circles: Parts and Equations

Identify parts of a circle.
Identify the center and radius of a circle from its equation.
Write the equation of a circle from its graph.

​But first,
Parts of a circle

Labelling

Label each part of the circle.

Drag labels to their correct position on the image

Tangent

Segment

Chord

Radius

Sector

Diameter

Circumference

Arc

Drag and Drop

What is the green line called?

Placeholder

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Circle

Radius

Diameter

Circumference

Dropdown

What is the blue line called?

Select answer

Multiple Choice

The distance around the perimeter of a circle is called

• Circle

• Radius

• Diameter

• Circumference

Drag and Drop

What is being represented in the image?

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Secant

Chord

Tangent

Inscribed Angle

Drag and Drop

What is being represented in the image?

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Curve

Chord

Arc

Partial

Dropdown

What is being represented in the image?

Select answer

Drag and Drop

What is being represented in the image?

Placeholder

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Arc

Chord

Central Angle

Concentric Circles

​Circle Equations

​the center is (0, 0) radius is 5

​5

​5

Dropdown

What is the center of the circle with the equation $$x^2+y^2=1$$ ?

Select answer

Drag and Drop

What is the radius of the circle with the equation $$x^2+y^2=16$$ ?

Placeholder

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Drag and Drop

Write the equation of the circle with the center (0,0) and radius: 9

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Drag and Drop

Write the equation of the circle with the center (0,0) and radius: 3

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Labelling

Label the following parts of a circle and it's equation.

Drag labels to their correct position on the image

Quadrant 1

Quadrant 2

x-coordinate

origin

coordinates

Quadrant 3

y-coordinate

radius

shazam

the equation of the circle has to be adjusted.

​

When you move the center,

Center moved from
(0, 0) to (1, 0) think right 1

 
The equation adjusts for the move by subtracting 1 (left 1)
so the center is back at the origin

​radius = 2

​(1, 0)

​

the equation of the circle has to be adjusted.

​

When you move the center,

Center moved from
(0, 0) to (0, 3) think up 3

 
The equation adjusts for the move by subtracting 3 (down 3)
so the center is back at the origin

​radius 2

the equation of the circle has to be adjusted.

​

When you move the center,

Center moved from
(0, 0) to (1, 2) think right 1, and up 2

 
The equation adjusts for the move by subtracting 1 (left 1) and subtracting 2 (down 2) so the center is back at the origin

​radius = 2

​(1, 2)

Drag and Drop

Write the equation of a circle with center (7, 0) with radius 3.

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Dropdown

Which equation represents a circle with a center at (0, 9) and a radius of 10?

Select answer

Drag and Drop

What is the equation of a circle with radius 4 and center (0, 8)?

Placeholder

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Labelling

Label the center,

the radius and

the equation

of this circle

Drag labels to their correct position on the image

radius

center

Center (-2, 6)
think left 2, up 6 from origin
Radius 5

​Adjustments need to be made when you move the circle.

(-2, 6)

​radius 5

The equation adjusts
right 2, down 6 to return to origin

Center (-2, -6)
think left 2, down 6 from origin
Radius 5

​Adjustments need to be made when you move the circle.

The equation adjusts
right 2, up 6 to return to origin

Center (2, -6)
think right 2, down 6 from origin
Radius 5

​Adjustments need to be made when you move the circle.

The equation adjusts
left 2, up 6 to return to origin

Multiple Choice

What is the equation of the circle?

• (x+1)² + (y +1)² = 3
• (x+1)² + (y -1)² = 3
• (x+1)² + (y +1)² = 9
• (x-1)² + (y -1)² = 9

Multiple Choice

What is the equation of the circle, with centre (-4,5) and radius 6 units?

• (x - 4)^2 + (y + 5)^2 = 6
• (x - 4)^2 + (y + 5)^2 = 36
• (x + 4)^2 + (y - 5)^2 = 6
• (x + 4)^2 + (y - 5)^2 = 36

Multiple Choice

Write the equation of the circle with center C( -5 , 8 ) and radius = 7

• ( x - 5 )² + ( y + 8 )² = 14

• ( x - 5 )² + ( y - 8 )² = 49

• ( x - 5 )² + ( y + 8 )² = 49

• ( x + 5 )² + ( y - 8 )² = 49

Multiple Choice

In the equation  $$(x-3)^2+(y-2)^2=16$$ , the center of the circle is...

• $$(3,2)$$  

• $$(-3,-2)$$  

• $$(-2,-3)$$  

• $$(2,3)$$  

Multiple Choice

In the equation  $$(x+2)^2+(y+3)^2=49$$ , the center of the circle is at .... 

• $$(2,3)$$  

• $$(3,2)$$  

• $$(-3,-2)$$  

• $$\left(-2,-3\right)$$  

Multiple Choice

Consider the circle equation shown below - identify the center and the radius

$$\left(x-6\right)^2+\left(y+2\right)^2=64$$

• $$\left(6,-2\right)\ and\ r=8$$

• $$\left(6,-2\right)\ and\ r=64$$

• $$\left(-6,2\right)\ and\ r=8$$

• $$\left(-6,2\right)\ and\ r=64$$

Multiple Choice

Consider the circle equation shown below - identify the center and the radius

$$\left(x+6\right)^2+\left(y-2\right)^2=64$$

• $$\left(6,-2\right)\ and\ r=8$$

• $$\left(6,-2\right)\ and\ r=64$$

• $$\left(-6,2\right)\ and\ r=8$$

• $$\left(-6,2\right)\ and\ r=64$$

Multiple Choice

Consider the circle equation shown below - identify the center and the radius

$$\left(x+3\right)^2+\left(y-4\right)^2=25$$

• $$\left(3,-4\right)\ and\ r=25$$

• $$\left(3,-4\right)\ and\ r=5$$

• $$\left(-3,4\right)\ and\ r=5$$

• $$\left(-3,4\right)\ and\ r=25$$

Multiple Choice

Consider the circle equation shown below - identify the center and the radius

$$\left(x-3\right)^2+\left(y+4\right)^2=25$$

• $$\left(3,-4\right)\ and\ r=25$$

• $$\left(3,-4\right)\ and\ r=5$$

• $$\left(-3,4\right)\ and\ r=5$$

• $$\left(-3,4\right)\ and\ r=25$$

Poll

I can identify parts of a circle.

• 💯

• 🙂

• 😐

• 😮

Poll

I can identify the center and radius of a circle from its equation.

• 💯

• 🙂

• 😐

• 😮

Poll

I can write the equation of a circle from its graph.

• 💯

• 🙂

• 😐

• 😮

Poll

I need more practice.

• 💯 20 or more problems from each topic

• 🙂about 15 problems from each topic

• I could take a test right now and only make a few mistakes

• I could teach a friend these topics and get 100% on a test.