Free Printable Circles, Ellipses, and Hyperbolas

1.

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

2.

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

3.

See Picture

a)

A

b)

B

c)

C

4.

a)

A

b)

B

c)

C

d)

D

5.

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

6.

What is the standard equation of a circle?

a)

(x-k)² + (y-h)² = r²

b)

(x+h)² + (y+k)² = r²

c)

(x-h)² + (y-k)² = r²

d)

(k-x)² + (h-y)² = r²

7.

What does (h,k) standard for in the standard circle equation?

a)

(h,k) is the center of the circle

b)

(h,k) is a point on the circle.

c)

(h,k) is a point that we guess and find

d)

(h,k) is the distance of the circle

8.

What does the r in the standard equation stand for?

a)

r is the distance of the circle

b)

r is the radius of the circle

c)

r is the x coordinate of the center of the circle

d)

r is the y coordinate of the center of the circle

9.

Identify the center and the length of a and b.

a)

C: (0,4) a= 25, b=4

b)

C: (0,0) a= 4, b=25

c)

C: (0,5) a= 2, b=5

d)

C: (0,0) a= 5, b=2

10.

Write an equation for the ellipse with each set of characteristics. Then answer the question.
Vertices ( 4, 3), (4, - 9)
Length of minor axis is 8
what is the center of this ellipse?

a)

(4, 6)

b)

( - 4, 3)

c)

(6, 4)

d)

(4, -3)

11.

The line containing the center and foci.

a)

Major Axis

b)

Minor Axis

c)

Vertices

d)

Co-Vertices

12.

Write an equation for the ellipse with each set of characteristics. Then answer the question.
co -Vertices ( -13, 7), (-3, 7)
Length of major axis is 16
what is the center of this ellipse?

a)

( - 8, 7)

b)

(7 , - 8)

c)

(8, -7)

d)

( - 7, 8)

13.

What are the foci of the shifted ellipse?

a)

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

b)

(±√3,0)

c)

(0,1) and (-6,1)

d)

(√3 - 3,1) and (-√3 - 3,1)

14.

What are the vertices of the shifted ellipse?

a)

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

b)

(0, 5) and (0, -5)

c)

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

d)

(0, 1) and (0, -1)

15.

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)

16.

How many Foci are there in an Ellipse

a)

0

b)

1

c)

2

d)

3

17.

What are the foci of the hyperbola with the equation y²/12 - x²/5 = 1

a)

(0, ±√17)

b)

(±√17, 0)

c)

(0, ±√7)

d)

(±√7, 0)

18.

What are the asymptotes of the hyperbola in the picture?

a)

y = x and y = –x

b)

y = 2x and y = –2x

c)

y = ¹/₂x and y = –¹/₂x

d)

y = 2x and y = 4x

19.

What are the vertices of the hyperbola?

a)

(0, 3) and (0, -3)

b)

(-4, 3) and (-4, -3)

c)

(0, 1) and (0, -1)

d)

(4, 0) and (-4, 0)

20.

A hyperbola has vertices (±5, 0) and one focus at (6, 0). What is the equation of the hyperbola in standard form?

a)

x²/25 + y²/11 = 1

b)

x²/5 - y²/11 = 1

c)

x²/11- y²/25 = 1

d)

x²/25 - y²/11= 1

21.

Find the equation of hyperbola.

a)

(x - 2)² / 16 - (y + 3)² / 20 = 1

b)

(x + 3)² / 16 - (y - 2)² / 20 = 1

c)

(x - 2)² / 20 - (y + 3)² / 16 = 1

d)

(y + 3)² / 16 - (x - 2)² / 20 = 1

23-24.

Answer the questions below after watching the video

23.

What is the equation relating a, b, and c in hyperbolas?

a)

c^2 = a^2 - b^2

b)

a^2 = b^2 + c^2

c)

b^2 = a^2 - c^2

d)

c^2 = a^2 + b^2

24.

What are the asymptotes of a hyperbola centered at the origin?

a)

y = ±b/a x

b)

x = ±b/a y

c)

y = ±a/b x

d)

x = ±a/b y

22.

The equation of the hyperbola, in standard form is . . .

a)

A

b)

B

c)

C

d)

D

25.

Answer the questions below after watching the video

25.

Given a circle's center at (-4, 5) and a radius of 3, what is the standard form equation of the circle?

a)

(x + 4)^2 + (y - 5)^2 = 3

b)

(x - 4)^2 + (y + 5)^2 = 3

c)

(x - 4)^2 + (y + 5)^2 = 9

d)

(x + 4)^2 + (y - 5)^2 = 9

26.

Which conic section is represented by the equation

x² + y² - 10x - 4y - 21 = 0

a)

Circle

b)

Ellipse

c)

Hyperbola

d)

Parabola

27.

Which conic section is represented by the equation

4x² + 25y² - 8x + 150y + 129 = 0

a)

Circle

b)

Ellipse

c)

Hyperbola

d)

Parabola

28.

Which conic section is represented by the equation

9x² - 4y² - 54x - 40y - 55 = 0

a)

Circle

b)

Ellipse

c)

Hyperbola

d)

Parabola

29.

Which conic section is represented by the equation

2x² - 16x - 12y + 20 = 0

a)

Circle

b)

Ellipse

c)

Hyperbola

d)

Parabola

30.

What is the value of a² for the given hyperbola?

a)

1

b)

-2

c)

25

d)

16

31.

Which type of conic is:

137 + 6y = -3y² - 3x² + 24x

a)

Circle

b)

Ellipse

c)

Hyperbola

d)

Parabola

32.

Which type of conic is:

137 + 6y = 3y² - 3x² + 24x

a)

Circle

b)

Ellipse

c)

Hyperbola

d)

Parabola

33.

Put

x² + y² - 6x + 8y - 11 = 0 into center form.

a)

(x - 3)² + (y + 4)² = 11

b)

(x - 3)² + (y + 4)² = -14

c)

(x - 3)² + (y + 4)² = 36

d)

(x - 3)² + (y + 4)² = 18

34.

Determine the direction each parabola opens.

a)

Left

1.

$x=-\frac{1}{12}\left(y-6\right)^2-5$

b)

Right

2.

$x=2\left(y+3\right)^2-11$

c)

Up

3.

$y=\frac{1}{4}\left(x+9\right)^2+2$

d)

Down

4.

$y=-\left(x-8\right)^2+5$

35.

Use the equation $\frac{\left(x-5\right)^2}{16}+\frac{y^2}{49}=1$ to answer the questions below.

This equation represents a(n) (a) with a (b) major axis and whose center is (c) .

Choose from the below words

ellipse

hyperbola

$\left(5,\ 0\right)$

$\left(-5,\ 0\right)$

$\left(4,\ 7\right)$

vertical

horizontal

$\left(0,\ -5\right)$

$\left(-4,\ -7\right)$

diagonal

36.

Given: $x^2+y^2-24y+114=0$

The center of the circle is (a) and the radius is (b) .

Choose from the below words

$C\left(0,\ 12\right)$

$r=\ \sqrt[]{30}$

$C\left(0,\ -12\right)$

$C\left(-12,\ 0\right)$

$r=30$

$r=900$

$C\left(1,-12\right)$

$r=5\ \sqrt[]{6}$

38-42.

Answer the questions below after watching the video

38.

What is the formula for a hyperbola centered at the origin when x is squared first?

a)

y^2/a^2 - x^2/b^2 = 1

b)

x^2 + y^2 = 1

c)

x^2/a^2 - y^2/b^2 = 1

d)

y^2 + x^2 = 1

39.

How does the orientation of a hyperbola change when y is squared first in the equation?

a)

It becomes a circle

b)

It remains unchanged

c)

It opens up and down

d)

It opens left and right

40.

What is the equation for the asymptotes of a hyperbola centered at the origin?

a)

y = ±(a/b)x

b)

x = ±(a/b)y

c)

x = ±(b/a)y

d)

y = ±(b/a)x

41.

For a hyperbola not centered at the origin, what does (h, k) represent?

a)

The coordinates of the foci

b)

The direction of the asymptotes

c)

The coordinates of the center

d)

The length of the transverse axis

42.

How do you find the foci of a hyperbola?

a)

c^2 = a^2 + b^2

b)

c^2 = a^2 - b^2

c)

b^2 = a^2 + c^2

d)

a^2 = b^2 + c^2

37.

Write the standard form of a circle with

center $\left(0,\ -7\right)$ and has a radius of $7\ \sqrt[]{2}$ .

Circles, Ellipses, and Hyperbolas

Total questions: 37

Worksheet time: 11hrs 12mins

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