Free Printable 1B Completing the Square & Equation of a Circle Problems

1.

Which of the following is the correct equation of the given circle?

a)

(x+1)² + (y +1)² = 3

b)

(x+1)² + (y -1)² = 3

c)

(x+1)² + (y +1)² = 9

d)

(x-1)² + (y -1)² = 9

2.

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

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

3.

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

a)

4

b)

2

c)

16

d)

8

4.

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

a)

(3,2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

5.

What are the coordinates of the center and the radius of the given equation of a circle:

$\left(x+7\right)^2+\left(y-6\right)^2=64$ ?

a)

Center (7,-6)

Radius = 8 units

b)

Center (-7,6)

Radius = 64 units

c)

Center (-7,6)

Radius = 8 units

d)

Center (7,-6)

Radius = 64 units

6.

What is the equation of a circle whose diameter is 24 and whose center is at the origin?

a)

x²+y²=12

b)

x²+y²=24

c)

x²+y²=144

d)

x²+y²=576

7.

What is the equation of the circle with center (4,2) and radius of 5?

a)

(x + 4)² + (y + 2)² = 25

b)

(x + 4)² + (y + 2)² = 5

c)

(x - 4)² + (y - 2)² = 5

d)

(x - 4)² + (y - 2)² = 25

8.

What is the center of the circle with this equation is (x+2)²+(y-4)²=41?

a)

(2,-5)

b)

(-2,4)

c)

(2,-4)

d)

(-2, -4)

9.

What is the radius of the circle with this equation of (x-5)²+(y+7)²=8?

a)

4

b)

8

c)

4√2

d)

2√2

10.

Which graph corresponds to
(x)²+ (y-6)²=9

a)

A

b)

B

c)

C

d)

D

11.

What is the equation for the circle graphed?

a)

$\left(x+5\right)^2+\left(y+6\right)^2=2$

b)

$\left(x-5\right)^2+\left(y+6\right)^2=4$

c)

$\left(x+5\right)^2+\left(y-6\right)^2=2$

d)

$\left(x-5\right)^2+\left(y-6\right)^2=4$

12.

The point (-5,6) is on a circle with center (-1,3). Write the equation of the circle.

a)

(x+5)²+(y-6)²=5

b)

(x-5)²+(y+6)²=25

c)

(x-1)²+(y+3)²=5

d)

(x+1)²+(y-3)²=25

13.

Write the equation of a circle with a center at (-2,3) and a point on the circle at (-2,7).

a)

(x+2)²+(y-3)²=16

b)

(x+2)²+(y-3)²=4

c)

(x-2)²+(y+3)²=4

d)

(x-2)²+(y+3)²=16

14.

Write the equation of a circle with a center at (-2,1) and a point on the circle at (0,3).

a)

$\left(x+2\right)^2+\left(y-1\right)^2=8$

b)

$\left(x-2\right)^2+\left(y+1\right)^2=8$

c)

$\left(x+2\right)^2+\left(y-1\right)^2=\sqrt{8}$

d)

$\left(x-2\right)^2+\left(y+1\right)^2=\sqrt{8}$

15.

What is the equation for this circle?

a)

(x+1)²+(y+3)²=9

b)

(x-1)²+(y-3)²=3

c)

(x-1)²+(y-3)²=9

d)

(x+1)²+(y+3)²=3

16.

Complete the square to write the equation of this circle in standard form. $-6y\ +x^2\ +y^2\ +18x-10=100$

a)

$\left(x-3\right)^2+\left(y+9\right)^2=100$

b)

$\left(x+9\right)^2+\left(y-3\right)^2\ =\ 100$

c)

$\left(x-3\right)^2+\left(y-18\right)^2\ =\ 200$

d)

$\left(x+9\right)^2+\left(y-3\right)^2=200$

17.

$x^2+10x+y^2+8y=59$ For the given equation, complete the square to determine the center and radius of the circle.

a)

center: (5,4), radius = 10

b)

center: (5, 4), radius = 100

c)

center: (-5, -4), radius = 100

d)

center: (-5, -4), radius = 10

18.

Complete the square to determine the equation of the circle in standard form:

x²+ y²+ 6x - 12y + 20 = 0

a)

(x-3)² + (y+6)² = 25

b)

(x+3)² + (y-6)² = 25

c)

(x-3)² + (y+6)² = 45

d)

(x+3)² + (y-6)² = 5

19.

Is the point (-3 , 5) inside, outside or on the circle with equation (x+2)² + (y-4)² = 9?

a)

Inside the Circle

b)

Outside the Circle

c)

On the Circle

20.

An earthquake occurred at the coordinate (-10,30) and could be felt in cities within a radius of 200 miles. Determine if a city located at the coordinate (150, -88) was within the boundary, on the boundary or outside the boundary for feeling the earthquake.

a)

Within the boundary

b)

On the boundary

c)

Outside the boundary

21.

Find the last term:

x^2+22x+c

a)

22

b)

11

c)

121

d)

44

22.

Find the last term:

x^2-8x+c

a)

8

b)

4

c)

-16

d)

16

23.

Find the last term:

x^2-16x+c

a)

8

b)

64

c)

-16

d)

16

24.

Find the last term:

x^2+34x+c

a)

289

b)

17

c)

34

d)

-34

25.

Find the last term:

x^2+30x+c

a)

30

b)

15

c)

225

d)

-15

26.

Find the last term:

x^2+4x+c

a)

4

b)

2

c)

-2

d)

-4

27.

Find the last term:

x^2-6x+c

a)

-9

b)

9

c)

6

d)

-6

28.

Find the last term:

x^2+10x+c

a)

5

b)

2

c)

20

d)

25

29.

Find the last term:

x^2+12x+c

a)

36

b)

21

c)

16

d)

25

30.

Find the last term:

x^2+42x+c

a)

-9

b)

21

c)

441

d)

1764

31.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

32.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

33.

Complete the Square
x² + 6x = 5

a)

(x + 3)² = 5

b)

(x + 6)² = 9

c)

(x + 3)² = 14

d)

(x + 6)² = 14

34.

Complete the Square
x² + 6x = 5

a)

(x + 3)² = 5

b)

(x + 6)² = 9

c)

(x + 3)² = 14

d)

(x + 6)² = 14

35.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

36.

Batman is a part of what comic franchise?

a)

DC

b)

Marvel

37.

What year was the Declaration of Independence signed?

a)

1777

b)

1776

c)

1806

d)

1774

38.

Reorder the following from first event to last

a)

American Revolutionary War

b)

War of 1812

c)

Spanish American War

d)

WWI

e)

Cold War

1)

2)

3)

4)

5)

39.

Label the Characters

a)Woody

b)Buzz Lightyear

c)Bo Peep

1

2

3

1)

2)

3)

40.

(a) led the Montgomery Bus Boycott?

Choose from the below words

Martin Luther King, Jr.

Malcolm X

Rosa Parks

Harriet Tubman

41.

Who was the third president of the United States?

a)

Abraham Lincoln

b)

Donald Trump

c)

George Washington

d)

Thomas Jefferson

42.

WALL-E: What does WALL-E stand for?

a)

World Administration Life Locator Electrical

b)

Waste Allocation Load Lifter Earth-Class

c)

Waste Alien Location Lever Electrifier

d)

Weird Aliens Love Laughing at Earth

43.

Moana: What's the name of this bling-loving crab?

a)

Hei Hei

b)

Tamatoa

c)

Tui

d)

Maui

44.

Coco: What is Miguel's canine companion called?

a)

Rover

b)

Fang

c)

Jeff

d)

Dante

45.

Inside Out: What is this thoroughly reasonable character called?

a)

Fear

b)

Joy

c)

Sadness

d)

Anger

46.

Despicable Me: How many sisters does Agnes have?

a)

1

b)

2

c)

3

d)

4

47.

The Incredibles 2: What is the name of Lucius Best's superhero character?

a)

The Ice Man

b)

Frosty the Destroyer

c)

Snowman

d)

Frozone

48.

The Lion King: What's the name of Simba's nasty uncle?

a)

Scar

b)

Jafar

c)

Gaston

d)

Shere Khan

49.

Beauty and the Beast: What are these two characters called?

a)

Waxy and Clockman

b)

Lumiere and Cogsworth

c)

Flicker and Ticker

d)

Flame and Tock

50.

who sang "I Want It That Way"?

a)

NYSNC

b)

Backstreet Boys

c)

One Direction

d)

NKOTB

1B Completing the Square & Equation of a Circle Problems

Total questions: 50

Worksheet time: 3hrs 30mins

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