Deck 6: Topics in Analytic Geometry

Question 1

Find the vertex and focus of the parabola.

Answer 1

A

Question 2

Select the graph of the following equation

Answer 2

B

Question 3

Consider a line with slope m and y-intercept Select the graph of the distance between the origin and the line.

Answer 3

D

Question 4

Convert the rectangular equation to polar form. Assume

Question 5

A point in rectangular coordinates is given. Convert the point to polar coordinates.

Question 6

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

Question 7

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

Question 8

Select the graph for following equation.

Question 9

Find the center, vertices and foci of the hyperbola.

Question 10

Select the curve represented by the parametric equations.

Question 11

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.

Question 12

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.

Question 13

Convert the polar equation to rectangular form.

Question 14

Select the correct graph of the following equations of the hyperbola and find the cen- ter of the hyperbola.

Question 15

Select the correct equation of the following graph.

Question 16

Find the slope of the line with inclination . Round your answer to four decimal places.

Question 17

Find the Eccentricity of the conic.

Question 18

Find the distance between the point and the line. Round your answer to four decimal places.

Question 19

Find the standard form of the equation of the ellipse with the given characteristics.

Question 20

Select the curve represented by the parametric equations. (indicate the orientation of the curve)

Question 21

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.

Question 22

Select the curve represented by the parametric equations. (indicate the orientation of the curve)

Question 23

Identify the conic and select its correct graph.

Question 24

Select the curve represented by the parametric equations.

Question 25

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

Question 26

Select the polar equation with graph.

Question 27

Consider a line with slope m and y-intercept Select the graph of the distance between the origin and the line.

Question 28

Find the distance between the point and the line. Round your answer to four decimal places.

Question 29

Select the correct equation of the following graph.

Question 30

Select the graph for following equation.

Question 31

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.

Question 32

Select the graph of the following equation

Question 33

Find the Eccentricity of the conic.

Question 34

Find the center, vertices and foci of the hyperbola.

Question 35

Find the slope of the line with inclination . Round your answer to four decimal places.

Question 36

Identify the conic and select its correct graph.

Question 37

Find the standard form of the equation of the ellipse with the given characteristics.

Question 38

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.

Question 39

Select the correct graph of the following equations of the hyperbola and find the cen- ter of the hyperbola.

Question 40

Find the vertex and focus of the parabola.

Question 41

Find the standard form of the equation of the parabola with the given characteristics.

Question 42

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

Question 43

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.

Question 44

Identify the conic and select its correct graph.

Question 45

Find the inclination (in degrees) of the line with a slope of . Round your answer to one decimal places.

Question 46

A point in rectangular coordinates is given. Convert the point to polar coordinates.

Question 47

Identify the conic and select its correct graph.

Question 48

Consider a line with slope m and y-intercept Write the distance d between the point and the line as a function of m.

Question 49

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.

Question 50

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin.

Question 51

Find the distance between the point and the line. Round your answer to four decimal places.

Question 52

Give the standard form of the equation of the parabola with the given characteristics.

Question 53

Convert the polar equation to rectangular form.

Question 54

Convert the rectangular equation to polar form. Assume

Question 55

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

Question 56

Find the center and vertices of the ellipse.

Question 57

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.

Question 58

Identify the conic as a circle or an ellipse then find the radius.

Question 59

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.

Question 60

Select the polar equation with graph.

Question 61

Find the distance between the point and the line. Round your answer to four decimal places.

Question 62

Identify the conic and select its correct graph.

Question 63

Find the standard form of the equation of the parabola with the given characteristics.

Question 64

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

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

Question 65

Convert the rectangular equation to polar form. Assume

Question 66

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.

Question 67

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

Question 68

Find the inclination (in degrees) of the line with a slope of . Round your answer to one decimal places.

Question 69

Convert the polar equation to rectangular form.

Question 70

Find a polar equation of the conic with its focus at the pole.

Question 71

Select the graph of over the interval. Describe the part of the graph ob- tained in this case.

Question 72

A point in rectangular coordinates is given. Convert the point to polar coordinates.

Question 73

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.

Question 74

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

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

Question 75

By using a graphing utility select the correct graph of the polar equation. Identify the graph.

Question 76

Consider a line with slope m and y-intercept Write the distance d between the point and the line as a function of m.

Question 77

Using following result find a set of parametric equation of the line.

Question 78

Select the parametric equations matching with the following graph.

Question 79

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.

Question 80

Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places.