Deck 10: Conic Sections and More Graphing

Question 1

Find the equation of the circle that satisfies the following conditions. Express the final equation in the form x ² + y ² + Dx + Ey + F = 0. Center at (0, -1) and r = 6

A) x ² + y ² - 2 y - 37 = 0
B) x ² + y ² - 2 y + 1 = 0
C) x ² + y ² + 2 y - 35 = 0
D) x ² + y ² + 2 y + 1 = 0

Answer 1

x ² + y ² + 2 y - 35 = 0

Question 2

Select the graph of the ellipse.

A)
B)
C)
D)
E)

Answer 2

Question 3

One section of a suspension bridge hangs between two towers that are 40 feet above the surface and 300 feet apart. A cable strung between the tops of the two towers is in the shape of a parabola with its vertex 20 feet above the surface. With axes drawn as indicated in the figure, find the equation of the parabola.

A) x ² - 563 y + 45,000 = 0
B) x ² - 1,125 y + 22,500 = 0
C) x ² - 695 y + 55,600 = 0
D) x ² - 1,390 y + 27,800 = 0
E) x ² - 1,100 y + 22,000 = 0

Answer 3

x ² - 1,125 y + 22,500 = 0

Question 4

A parabolic arch spans a stream 220 feet wide. How high above the stream must the arch be to give a minimum clearance of 20 feet over a channel in the center that is 180 feet wide?

A) 20 feet
B) 31.325 feet
C) 60.5 feet
D) 80.5 feet
E) 34.725 feet

Question 5

Find the center and the length of a radius of the circle. x ² + y ² - 8 x + 2 y = 0

A)
B)
C)
D)
E)

Question 6

Write the equation of the circle that satisfies the following conditions. Express the final equation in the form x ² + y ² + Dx + Ey + F = 0. Center at the origin and r = 4

A) x ² + y ² = 0
B) x ² - y ² - 16 = 0
C) x ² - y ² + 16 = 0
D) x ² + y ² + 16 = 0
E) x ² + y ² - 16 = 0

Question 7

Refer to the illustration. How far does a point on the tip of a rotor blade travel when it makes one complete revolution? The length of the blade is equal to 17 feet.

A)
B)
C)
D)
E)

Question 8

Find the center and radius of a circle given an equation in standard form.

A)
B)
C)
D)

Question 9

If the orbit of the comet is approximated by the equation , how far is it from the sun at the vertex of the orbit? Distances are measured in astronomical units (AU). __________ AU

Question 10

Find the equation of the circle that satisfies the following conditions. Express the final equation in the form x ² + y ² + Dx + Ey + F = 0. Tangent to the x axis, a radius of length 2, and abscissa of center is -1

A) x ² + y ² - 2 x - 4 y + 1 = 0 and x ² + y ² - 2 x + 4 y + 1 = 0
B) x ² + y ² + 2 x - 4 y + 1 = 0
C) x ² + y ² + 2 x - 4 y + 1 = 0 and x ² + y ² + 2 x + 4 y + 1 = 0
D) x ² + y ² + 2 x + 4 y + 1 = 0
E) x ² + y ² - 2 x + 4 y + 1 = 0

Question 11

Joan wants to jog miles on a circular track mile in diameter. How many times must she circle the track?

A) 45.84
B) 11.46
C) 22.92
D) 5.73
E) 2.86

Question 12

Find the length of a radius of this circle. x ² + y ² = 13

A)
B)
C)
D)
E)

Question 13

Graph the equation.

A)
B)
C)
D)
E)

Question 14

Find the center and radius of a circle given an equation in standard form.

A) C (0, 0),
B) C (0, 0),
C) C (0, 0),
D) C (0, 5),

Question 15

Find the center and radius of a circle given an equation in standard form.

A)
B)
C)
D)

Question 16

Find the vertex of the parabola and graph it.

A)
B)
C)
D)
E)

Question 17

Find the vertex of the parabola and graph it.

A)
B)
C)
D)
E)

Question 18

Suppose the two "legs" of the compass shown in the illustration are adjusted so that the distance between the pointed ends is 3 inches. What will the area of the circle be, if ?

A) 28.26
B) 18.84
C) 3.1415926536
D) 6
E) none of these

Question 19

Find the center and the length of a radius of the circle. x ² + y ² - 2 x - 6 y + 1 = 0

A) (-1, -3), r = 3
B) (3, -1), r = 6
C) (1, 3), r = 6
D) (3, 1), r = 3
E) (1, 3), r = 3

Question 20

Find the vertex of the parabola and graph it.

A)
B)
C)
D)
E)

Question 21

Solve the system of equations by graphing.

A)
B)
C)
D)
E)

Question 22

The elliptical track in the illustration is bounded by the ellipses and Find the area of the track. ( Hint : The area of an ellipse is .)

A)
B)
C)
D)
E)

Question 23

Graph the equation.

A)
B)
C)
D)
E)

Question 24

Graph the equation.

A)
B)
C)
D)
E)

Question 25

Graph the hyperbola.

A)
B)
C)
D)
E)

Question 26

The particle shown in the illustration approaches the nucleus at the origin along the path How close does the particle come to the nucleus?

A) 7 units
B) 8 units
C) 4 units
D) 9 units
E) 6 units

Question 27

Write the equation in standard form.

A)
B)
C)
D)
E)

Question 28

Two similarly charged particles are shot together for an almost head-on collision, as in the illustration. They repel each other and travel the branches of the hyperbola given by How close do they get?

A) 24 units
B) 21 units
C) 22 units
D) 18 units
E) 25 units

Question 29

Graph the equation.

A)
B)
C)
D)
E)

Question 30

What is the equation of the outer edge of the pool table displayed below, if l = 56 and w = 36?

A)
B)
C)
D)

Question 31

Graph the hyperbola.

A)
B)
C)
D)
E)

Question 32

Select the graph of the ellipse.

A)
B)
C)
D)
E)

Question 33

Select the graph of the ellipse.

A)
B)
C)
D)
E)

Question 34

Graph the hyperbola.

A)
B)
C)
D)
E)

Question 35

Graph the hyperbola.

A)
B)
C)
D)
E)

Question 36

By determining the difference of the distances between the ship shown in the illustration and two radio transmitters, the LORAN system places the ship on the hyperbola If the ship is also 5 miles out to sea, find its coordinates.

A) (21, 5)
B) (25, 5)
C) (22, 5)
D) (20, 5)
E) (26, 5)

Question 37

Graph the equation.

A)
B)
C)
D)
E)

Question 38

Graph the equation.

A)
B)
C)
D)
E)

Question 39

Graph the equation.

A)
B)
C)
D)
E)

Question 40

The arch of the underpass in the picture is a part of an ellipse. Find the equation of the arch.

A)
B)
C)
D)
E)

Question 41

Graph the function. f ( x ) = [ x ]

A)
B)
C)
D)
E)

Question 42

Graph the function.

A)
B)
C)
D)
E)

Question 43

Solve the system of equations algebraically for real values of and .

Question 44

Graph the function. f ( x ) = - [ x ] - 1

A)
B)
C)
D)
E)

Question 45

Solve the system of equations by graphing.

A)
B)
C)
D)
E)

Question 46

Graph the function and give the intervals on which F ( x ) is increasing, decreasing, or constant.

A) constant on (-5, 0) increasing on (0, 5)
B) constant on increasing on
C) constant on increasing on
D) constant on increasing on
E) constant on increasing on

Question 47

Solve the system of equations algebraically for real values of and .

A)
B)
C)
D)
E)

Question 48

Solve the system of equations by graphing.

A)
B)
C)
D)
E)

Question 49

Solve the system of equations algebraically for real values of and .

A)
B)
C)
D)
E)

Question 50

A marina charges $20 to rent a jet ski for 1 hour, plus $10 for every extra hour (or portion of an hour). In the illustration, h represents the number of hours and c represents the cost. Find the cost if the ski is used for 2.5 hours.

A) $40
B) $30
C) $45
D) $55
E) $60

Question 51

Computer access to international data network A costs $10 per day plus $8 per hour or fraction of an hour. Network B charges $15 per day, but only $6 per hour or fraction of an hour. In the illustration, t represents the connect time and C represents the total cost for each network. Find the minimal daily usage (in hours) after which it would be more economical to use network B.

A) After 2.5 hours, network B is cheaper.
B) After 1.5 hours, network B is cheaper.
C) After 2 hours, network B is cheaper.
D) After 1 hour, network B is cheaper.
E) After 3 hours, network B is cheaper.

Question 52

A cab company charges $3 for a trip up to 1 mile, and $2 for every extra mile (or portion of a mile). In the illustration, m represents the number of miles traveled and c represents the cost. Find the cost to ride miles.

A) $34
B) $26
C) $19
D) $29
E) $14

Question 53

Graph the function and give the intervals on which F ( x ) is increasing, decreasing, or constant.

A) increasing on (-∞, 1) constant on (1, ∞)
B) increasing on (-∞, 1) constant on (1, ∞)
C) decreasing on (-∞, 0) increasing on (0, 1) constant on (1, ∞)
D) decreasing on (-∞, 0) increasing on (0, 1) constant on (1, ∞)
E) increasing on (-∞, 0) decreasing on (0, ∞)

Question 54

Solve the system of equations algebraically for real values of and .

A)
B)
C)
D)
E)

Question 55

Solve the system of equations algebraically for real values of and

A)
B)
C)
D)
E)

Question 56

Solve the system of equations algebraically for real values of and .

A)
B)
C)
D)
E)

Question 57

Graph the function and give the intervals on which F ( x ) is increasing, decreasing, or constant.

A) increasing on decreasing on increasing on
B) increasing on decreasing on increasing on
C) increasing on decreasing on increasing on
D) decreasing on increasing on decreasing on
E) increasing on decreasing on [0, 1) increasing on