Find the center and the radius of the circle [image].
A.
Center (-2, 4), r = 4
B.
Center (2, -4), r = 4
C.
Center (-2, -4), r = 4
D.
Center (-2, 4), r =16
Definition
a
Term
Find the equation for the ci
rcle with radius 4 and center at (0, 0).
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
b
Term
Determine the opening direction of the parabola [image].
A.
Left
B.
Right
C.
Up
D.
Down
Definition
answer to the right
When the equation of a parabola is in the form y = a(x − h)2 + k, where a=14c , the graph of the parabola has the following characteristics:
Opens upward if a > 0; opens downward if a < 0
Vertex = (h, k)
xAxis of symmetry has equation x = h
Focus = (h, k [image]c)
Directrix has the equation y = h [image] c, depending upon the direction of the parabola
When the equation of a parabola is in the form x = a(y − k)2+ h, where
a=14c the graph of the parabola has the following characteristics:
Opens to the right if a > 0; opens to the left if a < 0
Vertex = (h, k)
Axis of symmetry has equation y = k
Focus = (h [image] c, k), depending upon the direction of the parabola
Directrix has the equation x = h [image] c, depending upon the direction of the parabola
Term
Find the equation for the circle with radius 2 and center at (4, -5).
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
b
Term
Find the center and the radius of the circle [image].
A.
Center (-2, 4), r = [image]
B.
Center (2, -4), r = [image]
C.
Center (-2, -4), r = [image]
D.
Center (-2, -4), r = [image]
Definition
a
Term
Determine the opening direction of the parabola [image].
A.
Left
B.
Right
C.
Up
D.
Down
Definition
d
Term
Which of the following is the sketch of x2/64 + y2/64 = 1?
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
c
Term
Determine the opening direction of the parabola[image].
A.
Left
B.
Right
C.
Up
D.
Down
Definition
left
When the equation of a parabola is in the form y = a(x − h)2 + k, where a=14c , the graph of the parabola has the following characteristics:
Opens upward if a > 0; opens downward if a < 0
Vertex = (h, k)
xAxis of symmetry has equation x = h
Focus = (h, k [image]c)
Directrix has the equation y = h [image] c, depending upon the direction of the parabola
When the equation of a parabola is in the form x = a(y − k)2+ h, where
a=14c the graph of the parabola has the following characteristics:
Opens to the right if a > 0; opens to the left if a < 0
Vertex = (h, k)
Axis of symmetry has equation y = k
Focus = (h [image] c, k), depending upon the direction of the parabola
Directrix has the equation x = h [image] c, depending upon the direction of the parabola
Term
Find the focus of the parabola[image].
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
a
When the equation of a parabola is in the form y = a(x − h)2 + k, where a=14c
Term
Determine the opening direction of the parabola [image].
A.
Left
B.
Right
C.
Up
D.
Down
Definition
up
Term
assignment number 2 unit 4
Given the equation of x2 -3xy + 2y2 + 2x - y + 6= 0, identify the graph of the equation.
A.
Circle
B.
Ellipse
C.
Hyperbola
D.
Parabola
Definition
c
Forms of Conic Sections
Circles, parabolas, ellipses, and hyperbolas are all forms of conic sections. The general form of a conic section is Ax2 + Bxy + cy2 + Dx + Ey + F = 0, where A, B and C are not all zero.
By looking at the coefficients A and C, we can determine which conic section the general form represents without having to put it in standard form. A is the coefficient of the x squared term, and C is the coefficient of the y squared term.
We have a(n):
Circle, if A = C.
Parabola, if A or C is equal to zero.
Ellipse, if A and C have the same sign, but are not equal.
Hyperbola, if A and C have opposite signs.
Example:
Identify the conic section represented by each equation.
3x2 − 2y2 − 4x + 5y = -3
A = 3, C = -2
Hyperbola, because they have opposite signs.
-4x2 − 4y2 + 6x +y = 5
A = -4, C = -4
Circle, because A = C.
8x2 + y2 + 3x − 7y = 0
A = 8, C = 1
Ellipse, because they have the same sign.
y2 − x + 3y − 9 = 0
A = 0, C = 1
Parabola, because A = 0.
Term
15Which of the following is the sketch of 4x2 + 9y2 = 36?
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
c
Term
Find the x-intercepts for the ellipse [image].
A.
(3, 0), (-3, 0)
B.
(2, 0), (-2, 0)
C.
(5, 0), (-5, 0)
D.
(13, 0), (-13, 0)
Definition
b
lengths 2a and 2b, respectively, where 0 <b < a, is
[image] [image]
Major axis is horizontal and parallel to the x-axis.
Center: (h, k) Foci: (h − c, k) and (h+ c, k) Major Axis: y = k Major Axis Vertices:(h − a, k) and (h + a, k) Minor Axis: x = h Minor Axis Vertices:(h, k − b) and (h, k + b)
[image] [image]
Major axis is vertical and parallel to the y-axis.
Center: (h, k) Foci: (h , k − c) and (h ,k + c) Major Axis: x = h Major Axis Vertices:(h , k − a) and (h , k +a) Minor Axis: y = k Minor Axis Vertices:(h − b, k) and (h + b, k)
When the center is the origin, the equations of an ellipse will take the following form.
[image]
Major axis is horizontal and parallel to the x-axis.
[image]
Major axis is vertical and parallel to the y-axis.
Term
Find the x-intercepts for the ellipse [image].
A.
(3, 0), (-3, 0)
B.
(5, 0), (-5, 0)
C.
(6, 0), (-6, 0)
D.
(10, 0), (-10, 0)
Definition
b
lengths 2a and 2b, respectively, where 0 <b < a, is
[image] [image]
Major axis is horizontal and parallel to the x-axis.
Center: (h, k) Foci: (h − c, k) and (h+ c, k) Major Axis: y = k Major Axis Vertices:(h − a, k) and (h + a, k) Minor Axis: x = h Minor Axis Vertices:(h, k − b) and (h, k + b)
[image] [image]
Major axis is vertical and parallel to the y-axis.
Center: (h, k) Foci: (h , k − c) and (h ,k + c) Major Axis: x = h Major Axis Vertices:(h , k − a) and (h , k +a) Minor Axis: y = k Minor Axis Vertices:(h − b, k) and (h + b, k)
When the center is the origin, the equations of an ellipse will take the following form.
[image]
Major axis is horizontal and parallel to the x-axis.
[image]
Major axis is vertical and parallel to the y-axis.
Term
Given the equation of 4x2 + 9y2 + 32x - 90y + 253= 0, identify the graph of the equation.
A.
Circle
B.
Ellipse
C.
Hyperbola
D.
Parabola
Definition
ellipse
Forms of Conic Sections
Circles, parabolas, ellipses, and hyperbolas are all forms of conic sections. The general form of a conic section is Ax2 + Bxy + cy2 + Dx + Ey + F = 0, where A, B and C are not all zero.
By looking at the coefficients A and C, we can determine which conic section the general form represents without having to put it in standard form. A is the coefficient of the x squared term, and C is the coefficient of the y squared term.
We have a(n):
Circle, if A = C.
Parabola, if A or C is equal to zero.
Ellipse, if A and C have the same sign, but are not equal.
Hyperbola, if A and C have opposite signs.
Example:
Identify the conic section represented by each equation.
3x2 − 2y2 − 4x + 5y = -3
A = 3, C = -2
Hyperbola, because they have opposite signs.
-4x2 − 4y2 + 6x +y = 5
A = -4, C = -4
Circle, because A = C.
8x2 + y2 + 3x − 7y = 0
A = 8, C = 1
Ellipse, because they have the same sign.
y2 − x + 3y − 9 = 0
A = 0, C = 1
Parabola, because A = 0.
Term
Given the equation of x2 -6xy + 9y2 + x - y - 1 = 0, identify the graph of the equation.
A.
Circle
B.
Ellipse
C.
Hyperbola
D.
Parabola
Definition
not ellipse of hyperbola
Forms of Conic Sections
Circles, parabolas, ellipses, and hyperbolas are all forms of conic sections. The general form of a conic section is Ax2 + Bxy + cy2 + Dx + Ey + F = 0, where A, B and C are not all zero.
By looking at the coefficients A and C, we can determine which conic section the general form represents without having to put it in standard form. A is the coefficient of the x squared term, and C is the coefficient of the y squared term.
We have a(n):
Circle, if A = C.
Parabola, if A or C is equal to zero.
Ellipse, if A and C have the same sign, but are not equal.
Hyperbola, if A and C have opposite signs.
Example:
Identify the conic section represented by each equation.
3x2 − 2y2 − 4x + 5y = -3
A = 3, C = -2
Hyperbola, because they have opposite signs.
-4x2 − 4y2 + 6x +y = 5
A = -4, C = -4
Circle, because A = C.
8x2 + y2 + 3x − 7y = 0
A = 8, C = 1
Ellipse, because they have the same sign.
y2 − x + 3y − 9 = 0
A = 0, C = 1
Parabola, because A = 0.
Term
Given the hyperbola x2/4 - y2/9 =1, find the foci.
A.
(-2, 0), (2, 0)
B.
([image], 0), (-[image], 0)
C.
(-3, 0), (3, 0)
D.
(0, -[image], (0, [image])
Definition
b
[image]
Click here for a long description of the image above.
Transverse axis is horizontal and parallel to the x-axis. Open left and right.
(x−h)2a2−(y−k)2b2=1
Center: (h, k)
Foci: [image]
c2=a2+b2
Vertices: [image]
Asymptotes: [image]
[image]
Click here for a long description of the image above.
Transverse axis is vertical and parallel to the y-axis. Open up and down.
(y−k)2a2−(x−h)2b2=1
Center: (h, k)
Foci: [image]
c2=a2+b2
Equation of Transverse Axis: [image]
Vertices: [image]
Asymptotes: [image]
Term
Given the hyperbola x2/4 - y2/9 =1, find the vertices.
A.
(-2, 0), (2, 0)
B.
(0, -2), (0, 2)
C.
(-3, 0), (3, 0)
D.
(0, -3), (0, 3)
Definition
a
[image]
Click here for a long description of the image above.
Transverse axis is horizontal and parallel to the x-axis. Open left and right.
(x−h)2a2−(y−k)2b2=1
Center: (h, k)
Foci: [image]
c2=a2+b2
Vertices: [image]
Asymptotes: [image]
[image]
Click here for a long description of the image above.
Transverse axis is vertical and parallel to the y-axis. Open up and down.
(y−k)2a2−(x−h)2b2=1
Center: (h, k)
Foci: [image]
c2=a2+b2
Equation of Transverse Axis: [image]
Vertices: [image]
Asymptotes: [image]
Term
Given the hyperbola x2/4 - y2/9 = 1, determine if the foci are on the x-axis or y-axis.
A.
x-axis
B.
y-axis
Definition
a
[image]
Transverse axis is on the y-axis.
[image]
Transverse axis is on the x-axis.
Term
Find the y-intercepts for the ellipse [image].
A.
(0, 3), (0, -3)
B.
(0, 2), (0, -2)
C.
(0, 5), (0, -5)
D.
(0, 13), (0, -13)
Definition
a
Term
Solve the system of equations. [image]
A.
[image]
B.
[image]
C.
[image]
D.
no solution
Definition
a
Identify each conic. Then solve the system of equations.
x2 − y2 = 5 2x2 + y2 = 22
x2 − y2 = 5 is the equation of a hyperbola.
2x2 + y2 = 22 is the equation of an ellipse.
There are, at most, 4 possible solutions.
Since the y2 terms have opposite signs, we can use elimination to solve for x.
x2 − y2 = 5
2x2 + y2 = 22
3x2 = 27 x2 = 9 x = ±3
Now, we will substitute 3 and -3 in for x and solve for y. Let's use the second equation.
2x2 y 2 = 22 2(3)2 + y 2 = 22 2(9) + y 2 =22 18 + y 2 = 22 y 2 = 4 y =±2
2x2 y 2 = 22 2(-3)2 + y 2 = 22 2(9) + y 2 =22 18 + y 2 = 22 y 2 = 4 y =±2
We get two solutions when x = 3, (3, 2) and (3, -2).
We also get two solutions when x = -3, (-3, 2) and (-3, -2).
There are 4 solutions, (3, 2),(3, -2), (-3, 2)to the system x2 −y 2 = 5. 2x2 + y2 = 22
We get two solutions when x = 3, (3, 2) and (3, -2).
We also get two solutions when x = -3, (-3, 2) and (-3, -2).
Term
Rewrite the following parametric equations by eliminating the parameter. x = 2t y = 4t2 + 4t - 1
A.
y = x2 + 2x - 1
B.
y = 2x2 + 4x - 1
C.
y = 4x2 + 4x - 1
D.
y = 8x3 + 8x2 - 1
Definition
a
Term
Rewrite the following parametric equations by eliminating the parameter. x = t y = -t2 + 3
A.
y = -x2 + 3
B.
y = (1/2)x2 + 3
C.
y = x2 - 3
D.
y = x2 + 3
Definition
a
Term
Solve the system of equations. [image]
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
d
Term
Rewrite the following parametric equations by eliminating the parameter. x = 3t - 1 y = [image]t
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
b
Term
Solve the system of equations. [image]
A.
[image]
B.
[image]
C.
[image]
D.
no solution
Definition
b
x=y+2
square it
x^2=y^2+4y
substitute
2y^2+4y-96=0
divide by 2
y^2+2y-48=0
(y+8)(y-6)=0
y=-8,0r 6
x-6, 8
Term
Solve the system of equations. [image]
A.
[image]
B.
[image]
C.
[image]
Click here for a long description of the image above.
D.
[image]
Definition
d
Term
Rewrite the following parametric equations by eliminating the parameter. [image]
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
b
Term
Solve the system of equations. [image]
A.
[image]
B.
[image]
C.
[image]
D.
no solution
Definition
b
Term
Rewrite the following parametric equations by eliminating the parameter. x = 3t2 y = 4t
A.
x = (3y2)/4
B.
x = (3y2)/16
C.
y = (3x2)/4
D.
y = (3x2)/16
Definition
b
Term
Given the equation x2 - y2 = 25, if you rotate the graph of the equation 45° about the origin, what is the new equation?
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
a
Term
Change the following polar coordinate into rectangular form. [image]
A.
([image]3, -1)
B.
([image]3, 1)
C.
(-[image]3, 1)
D.
(-[image]3, -1)
Definition
c
Change the following polar coordinates into rectangular form.
[image]
B(-4, 60°)
x = r cos[image] [image]
y= r sin[image] [image]
x = r cos[image] [image]
y = r sin[image] [image]
[image]
[image]
C
Term
Given the circle x2 + y2 = 16, if you translate the circle 5 units to the left and 4 units down, what is the new equation?
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
a
Term
Given the ellipse [image], if you rotate the ellipse 60° about the origin, what is the new equation?
A.
43(x')2 + 14x'y'√3 + 57(y')2 = 144
B.
43(x')2 + 14x'y'√3 + 57(y')2 = 576
C.
43(x')2 + 50x'y'√3 + 57(y')2 = 144
D.
43(x')2 + 50x'y'√3 + 57(y')2 = 576
Definition
b
Term
Which of the following does not represent the point (3, 60°)
A.
(-3, 600°)
B.
(3, -300°)
C.
(3, 240°)
D.
(3, 420°)
Definition
c
Term
Given the ellipse[image], if you translate the ellipse 3 units to the right and 8 units up, what is the new equation?
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
d
Term
Which of the following does not represent the point [image]?
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
C
Term
Which of the following does not represent the point [image]
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
D
Term
Which of the following does not represent the point (4, -75°)
A.
(-4, -615°)
B.
(4, -615°)
C.
(4, 285°)
D.
(4, 645°)
Definition
b
Term
Given the hyperbola [image], if you translate the hyperbola 6 units to the right and 3 units down, what is the new equation?
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
b
Term
Find the value of x. Round your answer to the nearest tenth. Drawing is not to scale.
[image]
A.
6.2 cm
B.
12.7 cm
C.
15.5 cm
D.
10.9 cm
| Save My Work | Next
Definition
A
Term
Find the value of x. Round to the nearest tenth. Drawing not to scale.
[image]
A.
12.9
B.
8.5
C.
12.4
D.
8.1
Prev | Save My Work | Next
Definition
D
Term
Find the value of x. Round to the nearest tenth. Drawing not to scale.
[image]
A.
41.2
B.
36.8
C.
46.6
D.
44.4
Definition
D
Term
What are the tangent ratios for the given angles? Angle P and Angle Q.
[image]
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
C
Term
Find the value of x to the nearest degree. Drawing is not to scale.
[image]
A.
67
B.
23
C.
83
D.
53
Prev | Save My Work | Next
Definition
B
Term
A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole casts a 249-foot-long shadow. Find the measure of angle A to the nearest degree.
[image]
A.
68o
B.
45o
C.
35o
D.
22o
Definition
D
Term
Select the equation tan 45o = 1 in the form of an inverse function.
A.
tan 1 = 45o
B.
cot 1 = 45o
C.
tan-11 = 45o
D.
[image]
Definition
Term
Find the missing value to the nearest tenth. tan___ = 45
A.
88.7o
B.
77.4o
C.
49.4o
D.
67.4o
Definition
A
Term
Find the value of x. Round your answer to the nearest tenth. Drawing is not to scale.
[image]
A.
3.5
B.
12.1
C.
6.1
D.
4
Definition
D
Term
What are the ratios for sinX and cosX?
[image]
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
C
Term
Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long. Round to the nearest degree.
A.
54o
B.
36o
C.
46o
D.
44o
Definition
B
Term
Use the graph to determine the period of this function.
[image]
A.
-1.95
B.
1.5
C.
3
D.
6
Definition
C
Term
A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an entrance door 9.3 feet from the desk. To the nearest degree, what is the angle of depression from the spotlight to the entrance door?
A.
37o
B.
39o
C.
51o
D.
53o
Definition
b
Term
An airplane over the Pacific sights an atoll at an angle of depression of 5. At this time, the horizontal distance from the airplane to the atoll is 4629 meters. What is the height of the plane to the nearest meter?
[image]
A.
403 m
B.
405 m
C.
4611 m
D.
4647 m
Definition
B
Term
Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long. Round to the nearest degree.
A.
54o
B.
36o
C.
46o
D.
44o
Definition
B
Term
To approach the runway, a small plane must begin a 9o descent starting from a height of 1125 feet above the ground. To the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this approach? (Hint: 1 mile = 5280 feet)
[image]
A.
1.3 mi
B.
1.4 mi
C.
0.2 mi
D.
7,191.5 mi
Definition
d
Term
The screen below shows the graph of a sound recorded on an oscilloscope. What is the period and the amplitude? (Each unit on the t-axis equals 0.01 seconds.)
[image]
A.
0.025 seconds, 4.5
B.
0.05 seconds, 4.5
C.
0.025 seconds, 9
D.
0.05 seconds, 9
Definition
B
Term
Find the period of the graph shown below.
[image]
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
C
Term
Evaluate and round your answer to the nearest hundredth. csc(-120o)
A.
0.58
B.
-0.87
C.
-1.15
D.
-2
Definition
C
Term
Determine whether the function shown below is or is not periodic. If it is, find the period.
[image]
A.
not periodic
B.
periodic; about 3
C.
periodic; about 2
D.
periodic; about 4
Definition
C
Term
Find the exact value. sec(-270o).
A.
0
B.
undefined
C.
1
D.
-1
Definition
B
Term
A sound wave has a period of 0.5 seconds and an amplitude of 2 units. Which of the following graphs represents the sound wave?
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
A
Term
Find the reference angle.
[image]
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
B
Term
Find the reference angle for 160o.
A.
-20o
B.
20o
C.
200o
D.
340o
Definition
B
Term
Find the reference angle for 1406o.
A.
-34o
B.
34o
C.
-146o
D.
146o
Definition
B
Term
Evaluate and round your answer to the nearest hundredth. sec(-600)
A.
2
B.
0.5
C.
-0.58
D.
-1.15
Definition
1
Term
ind the exact value. [image]
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
c
Term
If [image]
A.
240o
B.
225o
C.
210o
D.
200o
Definition
c
Term
Find the period, range and amplitude of the cosine function. [image]
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
d
Term
A particular sound wave can be graphed using the function. Find the amplitude and period of the function. [image]
A.
[image]
B.
[image]
C.
[image]
D.
[image]
Definition
a
Term
Use the Reference Angle Theorem to find the exact value of sin 225o.
