Circles: parts and equations

Presentation

•

Mathematics

•

9th - 12th Grade

•

Easy

•

CCSS

HSG.GPE.A.1, 6.NS.B.3, HSG.C.A.2

Standards-aligned

Susan Budde

Used 12+ times

FREE Resource

11 Slides • 30 Questions

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

Labeling

Label each part of the circle.

Drag labels to their correct position on the image

Arc

Diameter

Tangent

Segment

Sector

Chord

Radius

Circumference

Drag and Drop

What is the green line called?

Drag these tiles and drop them in the correct blank above

Circle

Radius

Diameter

Circumference

Dropdown

What is the blue line called?

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?

Drag these tiles and drop them in the correct blank above

Secant

Chord

Tangent

Inscribed Angle

Drag and Drop

What is being represented in the image?

Drag these tiles and drop them in the correct blank above

Curve

Chord

Arc

Partial

Dropdown

What is being represented in the image?

Drag and Drop

What is being represented in the image?

Drag these tiles and drop them in the correct blank above

Arc

Chord

Central Angle

Concentric Circles

Circle Equations

the center is (0, 0) radius is 5

Dropdown

What is the center of the circle with the equation

x^2+y^2=1

Drag and Drop

What is the radius of the circle with the equation

x^2+y^2=16

Drag these tiles and drop them in the correct blank above

Drag and Drop

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

Drag these tiles and drop them in the correct blank above

Drag and Drop

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

Drag these tiles and drop them in the correct blank above

Labeling

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

Drag labels to their correct position on the image

coordinates

Quadrant 1

origin

Quadrant 2

shazam

Quadrant 3

radius

x-coordinate

y-coordinate

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.

Drag these tiles and drop them in the correct blank above

Dropdown

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

Drag and Drop

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

Drag these tiles and drop them in the correct blank above

Labeling

Label the center,

the radius and

the equation

of this circle

Drag labels to their correct position on the image

center

radius

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.

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.

Show answer

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