Free Printable Parabolas and Circles

1.

What is the equation for the circle shown here?

a)

$\left(x-1\right)^2+\left(y+4\right)^2=16$

b)

$\left(x-1\right)^2+\left(y+4\right)^2=4$

c)

$\left(x+1\right)^2+\left(y-4\right)^2=4$

d)

$\left(x+1\right)^2+\left(y-4\right)^2=16$

2.

What is the standard form of the equation:
$x^2+y^2-10x+2y-10=0$ ?

a)

$\left(x-5\right)^2+\left(y+1\right)^2=16$

b)

$\left(x-5\right)^2+\left(y+1\right)^2=10$

c)

$\left(x-5\right)^2+\left(y+1\right)^2=6$

d)

$\left(x-5\right)^2+\left(y+1\right)^2=36$

3.

What is the vertex for the parabola:
$x=-2\left(y-3\right)^2+7$

a)

$\left(7,\ 3\right)$

b)

$\left(3,\ 7\right)$

c)

$\left(7,\ -3\right)$

d)

$\left(-3,\ 7\right)$

4.

What is the equation for the parabola shown in the image?

a)

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

b)

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

c)

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

d)

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

5.

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

6.

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

7.

Which of the following is the length of the diameter of the circle whose equation is shown below?
2x²+2y²-20x+24y=166

a)

12

b)

24

c)

6

d)

10

8.

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

9.

Which of the following is the correct equation for the given graph?

a)

f(x) = (x - 2)² - 1

b)

f(x) = (x + 2)² - 1

c)

f(x) = -(x + 2)² - 1

d)

f(x) = -(x - 2)² - 1

10.

What is the equation of a circle with radius 2 and center (3, 4)?

a)

(x+3)² + (y+4)² = 2

b)

(x-3)² + (y-4)² = 2

c)

(x+3)² + (y+4)² = 4

d)

(x-3)² + (y-4)² = 4

11.

What is the equation of the 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

12.

Which correctly describes the parabola: $y=-\frac{1}{2}\left(x+3\right)^2+4$

a)

Opens left

b)

Opens right

c)

Opens up

d)

Opens down

13.

Which correctly describes the parabola: $y=2\left(x-1\right)^2-3$

a)

Opens left

b)

Opens right

c)

Opens up

d)

Opens down

14.

What direction does the parabola point?

a)

Up

b)

Down

c)

Left

d)

Right

15.

(y-4)² = -8(x+1)
What direction does this parabola open?

a)

up

b)

down

c)

left

d)

right

16.

(x+3)² = 4(y+5)
What is the equation of the directrix?

a)

x = 4

b)

x = 2

c)

y = -4

d)

y = -6

17.

The focus is at (2,0) and the vertex is at (-4,0). What is the equation of the parabola?

a)

y² = 24(x+4)

b)

(y+4)² = -12x

c)

x² = 16(y+4)

d)

(x+4)² = -20y

18.

What is the equation of the directrix? (y - 4)²= -8(x+1)

a)

x = -3

b)

x = 1

c)

y = 6

d)

y = 2

19.

What is the equation of this parabola?

a)

(y-1)² = -4(x-3)

b)

(y-1)²= 4(x+3)

c)

(y+1)² = 4(x-3)

d)

(y+1)² = -4(x+3)

20.

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)

21.

In the equation (x-1)²+(y+4)²=9, the radius of the circle is...

a)

3

b)

9

c)

1

d)

4

22.

What is the vertex of the parabola $\left(y+5\right)^2=-12\left(x+4\right)$

a)

$\left(-5,-4\right)$

b)

$\left(5,4\right)$

c)

$\left(-4,\ -5\right)$

d)

$\left(4,5\right)$

23.

Find the vertex, focus, and directrix of the parabola with the given equation.

a)

vertex: (3, 2) focus: (5, 2) directrix: x = 1

b)

vertex: (-3, -2) focus: (-1, -2) directrix: x = -5

c)

vertex: (2, 3) focus: (4, 3) directrix: x = 0

d)

vertex: (3, 2) focus: (1, 2) directrix: x = 5

24.

Which conic section is represented by this equation?

a)

Circle

b)

Ellipse

c)

Hyperbola

d)

Parabola

25.

What is the directrix of the parabola

$\left(x-4\right)^2=8\left(y+3\right)$

a)

y = - 3

b)

x = 5

c)

y = - 5

d)

y = 2

26.

Find the equation of the figure shown.

a)

x = 1/4(y-4)²+2

b)

x = 1/8(y-3)²+4

c)

y = 1/6(x-3)²+4

d)

y = 1/4(x-3)²+4

27.

A circle has the equation $x^2+y^2-4x+12y-8=0$ . Use completing the square to write the equation in standard form.

a)

$\left(x-2\right)^2+\left(y+6\right)^2=48$

b)

$\left(x-6\right)^2+\left(y-2\right)^2=48$

c)

$\left(x+2\right)^2+\left(y+6\right)^2=48$

d)

$\left(x+2\right)^2+\left(y-6\right)^2=48$

Parabolas and Circles

Total questions: 27

Worksheet time: 2hrs 10mins

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