Free Printable Algebra 2 Test on Circles and Ellipses

1.

Find the distance between (-4, 5) and (7, 18).

Round to 2 decimal places.

a)

15.96

b)

16.08

c)

16.23

d)

17.03

2.

Identify the correct form of the distance formula.

a)

$d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\left(y_{2\ }-\ y_1\right)^2}\$

b)

$d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ -\ \left(y_{2_{\ }}-\ y_1\right)\ ^2}$

c)

$d\ =\ \sqrt{\left(y_{1\ }-\ y\ _2\right)^{ }\ +\ \left(x_{2\ }-\ x_1\right)}^{ }$

d)

$d=\sqrt{\left(x\right)^2-\ \left(y\right)^2}$

e)

$d=\sqrt{\left(x_1-y_1\right)+\left(x_2-y_2\right)^2}$

3.

What is the midpoint between (3, -1) and (7, -5)

a)

(5, -2)

b)

(10, -6)

c)

(5, -3)

d)

(2, -2)

4.

Find the midpoint: (-8, 6), (5, -7)

a)

$\left(-\frac{\text{3}}{2},-\frac{1}{2}\right)$

b)

$\left(\frac{3}{2},\frac{1}{2}\right)$

c)

$\left(7.5,7.5\right)$

d)

$\left(-2,-1\right)$

5.

Find the midpoint: $(9,1),(8,-4)$

a)

$\left(\frac{9}{2},\frac{5}{2}\right)$

b)

$\left(\frac{5}{2},\frac{9}{2}\right)$

c)

$\left(\frac{17}{2},-\frac{3}{2}\right)$

d)

$\left(-\frac{5}{2},\frac{17}{2}\right)$

6.

What is the other endpoint if one endpoint is (-4, 4) and

the midpoint is (-3, 3)?

a)

(2, -2)

b)

(-2, 2)

c)

(-1, 1)

d)

(-7, 7)

e)

(-3.5, 3.5)

7.

Which of the following is the correct midpoint formula given two endpoints (x₁, y₁) and (x₂, y₂)?

a)

b)

c)

d)

8.

Write the standard equation of the circle with the given center and radius; center (0, 0) and radius of 7.

a)

x²+ y²= 7

b)

x²+ y²= 14

c)

x²+ y²= 49

d)

x² -y²= 49

e)

x + y = 49

9.

What is the equation for this circle?

a)

x² + y² = 6

b)

x² + y² = 9

c)

x + y = 9

d)

x² + y² = 3

e)

x² + y² = 81

10.

What is the correct graph for the equation x² + y² = 4?

a)

b)

c)

d)

e)

11.

Write the standard equation of the circle with the given center (0, 0) and a point on the circle is (-6, -8).

a)

x²+ y²= 14

b)

x²+ y²= 10

c)

x²+ y²= 100

d)

x² +y²= 25

e)

x² + y² = 36

12.

A fire department services an area within an 8 mile radius of its station. A house was on fire 4 miles west and 7 miles south of the station. Is the house fire inside, outside or directly on the range (circle) of the service area for this fire department?

a)

Inside

b)

Outside

c)

Directly On

d)

Cannot be determined from the information given

13.

Identify the center and radius of the standard equation of the following circle...

x² + y² = 50

a)

(0, 0); 50

b)

(1, 1); 25

c)

(0, 0); $5\sqrt{2}$

d)

(0, 0); 100

e)

(1, 1); 10

14.

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

15.

What is the equation of the circle?

(I know it looks like an ellipse...... but it's not)

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

16.

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

a)

(-2,41)

b)

(-2,4)

c)

(2,-4)

d)

(2,41)

17.

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

a)

(x - 2)²+ (y + 5)²= 36

b)

(x - 5)² + (y + 2)² = 6

c)

(x + 5)²+ (y - 2)²= 36

d)

(x + 2)²+ (y - 5)²= 6

18.

In the circle represented by the equation (x-4)²+(y-3)²=25, the diameter is

a)

10

b)

3

c)

5

d)

25

19.

A circle has the equation
x² + y² - 12x + 8y + 3 = 0. Write the equation in standard form.

a)

(x - 6)² + (y + 4)² = 49

b)

(x + 4)² + (y - 6)² = 49

c)

(x - 6)² + (y + 4)² = 55

d)

x² + y² = 55

20.

Change the following equation to standard form
x²+y²-4x+12y-8=0

a)

(x+2)²+(y-6)²=48

b)

(x-2)²+(y+6)²=48

c)

(x-6)²+(y-2)²=48

d)

(x+2)²+(y-6)²=48

21.

Convert the equation of the circle from general to standard form.

a)

A

b)

B

c)

C

d)

D

22.

Select the matching graph.

a)

b)

c)

d)

23.

The equation of a circle is x²+ y²+ 6x - 12y + 20 = 0. Write the equation in standard form.

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

24.

A circle has the equation x² + y² + 10x - 4y + 20 = 0. Write it in standard form.

a)

(x - 5)² + (y + 2)² = 9

b)

(x + 5)² + (y - 2)² = 3

c)

(x + 5)² + (y - 2)² = 9

d)

(x - 5)² + (y + 2)² = 3

25.

Find the center and radius of the circle: x²+ y²+ 14x - 2y = -1.

a)

center = (-7, 2) radius = 3

b)

center = (-7, 1) radius = 7

c)

center = (-4, 1) radius = 7

d)

center = (-4, 2) radius = 3

26.

Find the equation of the graph:

a)

b)

c)

d)

27.

Find the length of the ellipse's major axis.

a)

3 units

b)

6 units

c)

9 units

d)

18 units

28.

Which of the following gives the standard form equation of a circle with center (-6, -4) and a radius of 16?

a)

(x + 6)² + (y + 4)² = 16²

b)

(x + 6)² + (y + 4)² = 16

c)

(x - 6)² + (y - 4)² = 16²

d)

(x - 6)² + (y - 4)² = 16

29.

Which is the equation of the circle graphed below?

a)

(x - 3)²+ (y + 4)² = 9

b)

(x - 3)²+ (y + 4)² = 3

c)

(x)²+ (y)² = 9

d)

(x - 1)²+ (y + 1)² = 7

30.

What are the coordinates of the center and the radius of the circle with equation:
(x - 4)² + (y - 3)² = 25 ?

a)

Center (4,3)
Radius = 5 units

b)

Center (4,3)
Radius = 25 units

c)

Center (-4,-3)
Radius = 25 units

d)

Center (-4,-3)
Radius = 5 units

31.

Is the major axis of the ellipse horizontal or vertical?

a)

horizontal

b)

vertical

c)

both

d)

neither

32.

What is the length of the minor axis?

a)

3

b)

6

c)

2

d)

4

33.

What is the center of the given equation?

a)

(4, 3)

b)

(-4, -3)

c)

(-4, 3)

d)

(4, -3)

34.

The major axis is:

a)

The shorter axis of an ellipse

b)

The longer axis of an ellipse

c)

The closest point closest to the Sun

d)

The farthest point closest to the Sun

35.

Determine the center and radius: x²+ y²+ 14x - 2y = -1

a)

center= (-7,2) radius= 3

b)

center= (-7,1) radius= 7

c)

center= (-4,1) radius= 5

36.

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

37.

Determine the equation of the circle in standard form:
x² + y² + 4x + 6y - 36 = 0

a)

(x+2)² + (y+3)² = 49

b)

(x+2)² + (y+3)² = 13

c)

(x-2)² + (y-3)² = 49

d)

(x-2)² + (y-3)² = 13

38.

Which of the following statements is false about the ellipse?

a)

The length of the minor axis is 4.

b)

The set of all x-values is [-6, 2].

c)

The y-intercepts are at (0, 2+ √3).

d)

The foci are at (-2 + 2√2, 2).

39.

Write the standard form of the ellipse:

9x² + 4y² + 72x + 108 = 0

a)

(x - 4)² / 16 + y ²/ 36 = 1

b)

(x + 4)² / 4 + y ²/ 9 = 1

c)

(x - 4)² / 4 + y ²/ 9 = 1

d)

(x + 4)² / 16 + y ²/ 36 = 1

40.

The line containing the center and foci.

a)

Major Axis

b)

Minor Axis

c)

Vertices

d)

Co-Vertices

41.

The major axis is...

a)

the x-axis

b)

the y-axis

c)

y = x

d)

y=-x

42.

In an ellipse, what is the length of the minor axis?

a)

a

b)

2a

c)

b

d)

2b

e)

c

43.

In an ellipse, what is the length of the major axis?

a)

a

b)

2a

c)

b

d)

2b

e)

c

44.

In an ellipse, what distance does c represent?

a)

The distance from the center to a vertex

b)

The distance from the center to a co-vertex

c)

The distance from the center to a focus

d)

The length of the minor axis

e)

The length of the major axis

45.

In an ellipse, what distance does b represent?

a)

The distance from the center to a vertex

b)

The distance from the center to a co-vertex

c)

The distance from the center to a focus

d)

The length of the minor axis

e)

The length of the major axis

46.

In an ellipse, what distance does a represent?

a)

The distance from the center to a vertex

b)

The distance from the center to a co-vertex

c)

The distance from the center to a focus

d)

The length of the minor axis

e)

The length of the major axis

47.

What are the vertices of the ellipse?

a)

(0, 0)

b)

(7, 1) and (-1, 1)

c)

(3, -5) and (3, 7)

d)

(3, 1)

48.

What are the co-vertices of the ellipse?

a)

(1, 5) and (1, -5)

b)

(0, 0) and (2, 0)

c)

(4, 0) and (6, 0)

d)

(1, 6) and (1, 4)

49.

What is the center, a and b values for the following equation:
x² + 4y² + 16x - 80y + 320 = 0

a)

(-8, 10); a = 12, b = 6

b)

(-8, 10); a = 6, b = 12

c)

(8, -10); a = 12, b = 6

d)

(8, -10); a = 6, b = 12

Algebra 2 Test on Circles and Ellipses

Total questions: 49

Worksheet time: 4hrs 58mins

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