Question 1

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph. ​   ​

Accepted Answer

A) Center: (0,0) Vertices: (-6,0)
​   
B) Center: (0,0) Vertices: (±6,0)
​   
C) Center: (0,0) Vertices: (-6,0)
​   
D) Center: (0,0) Vertices: (±6,0)
​   
E) Center: (0,0) Vertices: (6,0)
​   
A) Center: (0,0) Vertices: (-6,0)
​   
B) Center: (0,0) Vertices: (±6,0)
​   
C) Center: (0,0) Vertices: (-6,0)
​   
D) Center: (0,0) Vertices: (±6,0)
​   
E) Center: (0,0) Vertices: (6,0)
​

Question 2

Find the vertices and asymptotes of the hyperbola.

Accepted Answer

A) vertices: (±2,0), asymptote:   
B) vertices: (0,±2), asymptote:   
C) vertices: (±2,0), asymptote:   
D) vertices: (0,±2), asymptote:   
E) vertices: (±2,5), asymptote:   
A) vertices: (±2,0), asymptote:   
B) vertices: (0,±2), asymptote:   
C) vertices: (±2,0), asymptote:   
D) vertices: (0,±2), asymptote:   
E) vertices: (±2,5), asymptote:

Question 3

Select the polar equation of graph. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 4

Find a polar equation of the conic with its focus at the pole. ​
Conics
Eccentricity
Directrix
Ellipse     ​
​
​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

Sketch the graph of the ellipse, using the latera recta.
​   ​

Accepted Answer

The answer of Sketch the graph of the ellipse, using...

Question 6

Find the center and the vertices which located on the major axis of the ellipse.

Accepted Answer

A) center: (0, 0) vertices: (-9, 0), (9, 0) 
B) center: (0, 0) vertices: (0, -9), (0, 9) 
C) center: (-9, 9) vertices: (-1, 0), (1, 0) 
D) center: (0, 0) vertices: (-9, -1), (9, 1) 
E) center: (-9, 9) vertices: (-1, -9), (1, 9) 
A) center: (0, 0) vertices: (-9, 0), (9, 0) 
B) center: (0, 0) vertices: (0, -9), (0, 9) 
C) center: (-9, 9) vertices: (-1, 0), (1, 0) 
D) center: (0, 0) vertices: (-9, -1), (9, 1) 
E) center: (-9, 9) vertices: (-1, -9), (1, 9)

Question 7

Use a graphing utility to graph the parabola.   ​

Accepted Answer

The answer of Use a graphing utility to graph the...

Question 8

Find a set of parametric equations for the rectangular equation. ​     ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

Consider a line with slope m and y-intercept (0,5).Find the slope that yields the maximum distance between the origin and the line. ​

Accepted Answer

A) The maximum distance of   occurs when the slope m is   and the line through (0,5) is horizontal. 
B) The maximum distance of 5 occurs when the slope m is 0 and the line through (0,5) is horizontal. 
C) The maximum distance of   occurs when the slope m is 0 and the line through (0,5) is horizontal. 
D) The maximum distance of 6 occurs when the slope m is 0 and the line through (0,6) is horizontal. 
E) The maximum distance of   occurs when the slope m is   and the line through (0,5) is horizontal. 
A) The maximum distance of   occurs when the slope m is   and the line through (0,5) is horizontal. 
B) The maximum distance of 5 occurs when the slope m is 0 and the line through (0,5) is horizontal. 
C) The maximum distance of   occurs when the slope m is 0 and the line through (0,5) is horizontal. 
D) The maximum distance of 6 occurs when the slope m is 0 and the line through (0,6) is horizontal. 
E) The maximum distance of   occurs when the slope m is   and the line through (0,5) is horizontal.

Question 10

Identify the equation as a circle, a parabola, an ellipse, or a hyperbola. ​   ​

Accepted Answer

A) Ellipse 
B) Parabola 
C) Hyperbola 
D) Circle 
E) None of the above 
A) Ellipse 
B) Parabola 
C) Hyperbola 
D) Circle 
E) None of the above

Question 11

Find a polar equation of the conic with its focus at the pole. ​
Conics
Eccentrity
Directrix
Ellipse     ​​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Find the standard form of the equation of the hyperbola with the given characteristics. focies: (±4,0), asymptotes:

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

Find the center and vertices of the hyperbola.

Accepted Answer

A) center: (-2, -4), vertices: (-2, -6), (-2, -2) 
B) center: (2, 4), vertices: (2, 2), (2, 6) 
C) center: (2, 4), vertices: (0, 4), (4, 4) 
D) center: (-2, -4), vertices: (-4, -4), (0, -4) 
E) center: (-4, -2), vertices: (-6, -2), (-2, -2) 
A) center: (-2, -4), vertices: (-2, -6), (-2, -2) 
B) center: (2, 4), vertices: (2, 2), (2, 6) 
C) center: (2, 4), vertices: (0, 4), (4, 4) 
D) center: (-2, -4), vertices: (-4, -4), (0, -4) 
E) center: (-4, -2), vertices: (-6, -2), (-2, -2)

Question 14

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus:   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Using following result find a set of parametric equation of conic. ​
Circle:   ​
Circle: center:   ; radius: 5
​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places. ​   ​

Accepted Answer

A) Rectangular coordinates: (3.6,6.0) 
B) Rectangular coordinates: (5.5,2.4) 
C) Rectangular coordinates: (-5.5,-2.4) 
D) Rectangular coordinates: (-2.4,-5.5) 
E) Rectangular coordinates: (2.4,5.5) 
A) Rectangular coordinates: (3.6,6.0) 
B) Rectangular coordinates: (5.5,2.4) 
C) Rectangular coordinates: (-5.5,-2.4) 
D) Rectangular coordinates: (-2.4,-5.5) 
E) Rectangular coordinates: (2.4,5.5)

Question 17

Find the vertex, focus, and directrix of the parabola. ​   ​

Accepted Answer

A) Vertex:   ; Focus:   ; Directrix:   
B) Vertex:   ; Focus:   ; Directrix:   
C) Vertex:   ; Focus:   ; Directrix:   
D) Vertex:   ; Focus:   ; Directrix:   
E) Vertex:   ; Focus:   ; Directrix:   
A) Vertex:   ; Focus:   ; Directrix:   
B) Vertex:   ; Focus:   ; Directrix:   
C) Vertex:   ; Focus:   ; Directrix:   
D) Vertex:   ; Focus:   ; Directrix:   
E) Vertex:   ; Focus:   ; Directrix:

Question 18

Determine the angle   through which the axes are rotated.Round your answer to two decimal places. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

Find a set of parametric equations for the rectangular equation. ​   ​​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

Convert the rectangular equation to polar form.Assume r > 1. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph.

Find the vertices and asymptotes of the hyperbola.

Select the polar equation of graph.

Find a polar equation of the conic with its focus at the pole. Conics Eccentricity Directrix Ellipse

Sketch the graph of the ellipse, using the latera recta.

Find the center and the vertices which located on the major axis of the ellipse.

Use a graphing utility to graph the parabola.

Find a set of parametric equations for the rectangular equation.

Consider a line with slope m and y-intercept (0,5).Find the slope that yields the maximum distance between the origin and the line.

Identify the equation as a circle, a parabola, an ellipse, or a hyperbola.

Find a polar equation of the conic with its focus at the pole. Conics Eccentrity Directrix Ellipse

Find the standard form of the equation of the hyperbola with the given characteristics. focies: (±4,0), asymptotes:

Find the center and vertices of the hyperbola.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus:

Using following result find a set of parametric equation of conic. Circle: Circle: center: ; radius: 5

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places.

Find the vertex, focus, and directrix of the parabola.

Determine the angle through which the axes are rotated.Round your answer to two decimal places.

Find a set of parametric equations for the rectangular equation.

Convert the rectangular equation to polar form.Assume r > 1.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Exam 6: Topics-In-Analytic-Geometry

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph. ​ ​

Find the vertices and asymptotes of the hyperbola.

Select the polar equation of graph. ​ ​

Find a polar equation of the conic with its focus at the pole. ​ Conics Eccentricity Directrix Ellipse ​ ​ ​

Sketch the graph of the ellipse, using the latera recta. ​ ​

Find the center and the vertices which located on the major axis of the ellipse.

Use a graphing utility to graph the parabola. ​

Find a set of parametric equations for the rectangular equation. ​ ​

Consider a line with slope m and y-intercept (0,5).Find the slope that yields the maximum distance between the origin and the line. ​

Identify the equation as a circle, a parabola, an ellipse, or a hyperbola. ​ ​

Find a polar equation of the conic with its focus at the pole. ​ Conics Eccentrity Directrix Ellipse ​​

Find the standard form of the equation of the hyperbola with the given characteristics. focies: (±4,0), asymptotes:

Find the center and vertices of the hyperbola.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: ​

Using following result find a set of parametric equation of conic. ​ Circle: ​ Circle: center: ; radius: 5 ​

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places. ​ ​

Find the vertex, focus, and directrix of the parabola. ​ ​

Determine the angle through which the axes are rotated.Round your answer to two decimal places. ​ ​

Find a set of parametric equations for the rectangular equation. ​ ​​

Convert the rectangular equation to polar form.Assume r > 1. ​ ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph.

Select the polar equation of graph.

Find a polar equation of the conic with its focus at the pole. Conics Eccentricity Directrix Ellipse

Sketch the graph of the ellipse, using the latera recta.

Use a graphing utility to graph the parabola.

Find a set of parametric equations for the rectangular equation.

Consider a line with slope m and y-intercept (0,5).Find the slope that yields the maximum distance between the origin and the line.

Identify the equation as a circle, a parabola, an ellipse, or a hyperbola.

Find a polar equation of the conic with its focus at the pole. Conics Eccentrity Directrix Ellipse

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus:

Using following result find a set of parametric equation of conic. Circle: Circle: center: ; radius: 5

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places.

Find the vertex, focus, and directrix of the parabola.

Determine the angle through which the axes are rotated.Round your answer to two decimal places.

Find a set of parametric equations for the rectangular equation.

Convert the rectangular equation to polar form.Assume r > 1.