Deck 8: Analytic Geometry in Two and Three Dimensions

Question 1

What is the equation, in standard form, of the parabola with focus (3,0) and directrix x=-3 ?

Answer 1

Question 2

Determine the directrix of the conic with polar form

Answer 2

x= -6

Question 3

Use the discriminant to determine if is an ellipse, a parabola, or a hyperbola.

Answer 3

96>0 ; hyperbola

Question 4

What type of conic is the graph of

Question 5

Write the parametric equations for the line through the points (-1,2,4) and (6,0,-3) .

Question 6

Question 7

What is the equation of a parabola with vertex (-4,-4) that passes through (0,0) and has its axis of symmetry parallel to the y -axis?

Question 8

Find the coordinates of the point P(x, y)=(3,4) in the coordinate system x' y' obtained by a rotation of

Question 9

Find a polar equation for the conic with focus at (0,0) , eccentricity 4 / 3 , and directrix y=7 .

Question 10

What is the vertex of the parabola

Question 11

For the points A(-2,4,6), B(0,6,-2) and C(4,-8,6) , what is the distance from point A to the midpoint of line segment BC?

Question 12

Which of the following is the graph of the plane 2 x+6 y+z=1 ?

A)
B)
C)
D)

Question 13

Find an equation in standard form for the ellipse whose major axis endpoints are (-5,2) and (3,2) and whose minor axis has length 6 .

Question 14

After translation of coordinate axes, a quadratic
equation becomes
had the effect of moving the point (x, y)=(1,-2) to
the point
equation in x y coordinates?

A)
B)
C)
D)

Question 15

Find the foci of the ellipse

Question 16

Sketch a graph of the equation

Question 17

Find the asymptotes of the hyperbola

A)
B)
C)
D) y=2.06 x and y=-2.06 x

Question 18

Explain how you can use the eccentricity to determine whether the graph of a given quadratic equation is an ellipse or a circle.

Question 19

Find an equation in standard form for the hyperbola centered at (1,-4) , with one focus at (7,-4) and eccentricity e=2 .

Question 20

Which of the following are the vertices of the hyperbola

A) (3,8) and (3,-18)
B) (8,-5) and (-2,-5)
C) (3,8) and (3,-13)
D) (16,-5) and (-10,-5)

Question 21

What is the equation of the parabola with vertex (-2,-2) that passes through (0,0) and has its axis of symmetry parallel to the x -axis?

Question 22

Write the equation of the conic with focus (3,4) and directrix x=1 .

Question 23

In a whispering gallery, any sound at one focus of an ellipse reflects off the ellipse directly to the other focus. The figure shows an elliptical whispering gallery, where x is the center of the ellipse. What is the distance that sound travels from focus to focus

Question 24

The point (-3,-2,10) is what distance from the xz -plane?

A) -3
B) -2
C) 2
D) 3
E) 10

Question 25

Sketch the graph of the hyperbola in Problem 3.

Question 26

The point (-5,-4,8) is what distance from the y z -plane?

A) -5
B) -4
C) 4
D) 5
E) 8

Question 27

A telecommunications satellite is a paraboloid of revolution with a diameter of 8 ft and depth of 3 ft. How far from the vertex should the receiving antenna be placed?

Question 28

Identify the conic without drawing its graph. State the eccentricity and directrix.

Question 29

Question 30

What is the equation of the parabola with vertex (-4,-4) that passes through (0,0) and has its axis of symmetry parallel to the x -axis?

Question 31

For the equation in Problem 11, solve for y to obtain equation(s) that could be entered into your grapher.

Question 32

In three-dimensional space, what are the parametric equations for the line through the points (2,-1,3) and (-1,4,0)?

Question 33

Find a polar equation for an ellipse with a focus at (0,0) if the endpoints of its major axis have polar coordinates and

Question 34

Find the vertex of the parabola

Question 35

For the hyperbola
find the center, foci, endpoints of the transverse axis, and the equations of the asymptotes.

Question 36

In three-dimensional space, what is the equation of the set of points that are 12 units from the point (1,5,-4) ?

Question 37

Identify the type of conic given by the equation

Question 38

What is the magnitude of the vector

Question 39

Find the equation for the conic in standard form. Identify the conic.

Question 40

For the hyperbola find the center, foci, endpoints of the transverse axis, and the equations of the asymptotes.

Question 41

Identify the type of conic given by the equation

Question 42

In a whispering gallery, any sound at one focus of an ellipse reflects off the ellipse directly to the other focus. The figure shows an elliptical whispering gallery, where x is the center of the ellipse. What is the distance that sound travels from focus to focus

Question 43

In three-dimensional space, what is the equation of the set of points that are 8 units from the point (-3,5,2)?

Question 44

For the equation in Problem 11, solve for y to obtain equation(s) that could be entered into your grapher.

Question 45

Identify the conic without drawing its graph. State the eccentricity and directrix.

Question 46

A telecommunications satellite is a paraboloid of revolution with a diameter of 6 ft and depth of 3 ft. How far from the vertex should the receiving antenna be placed?

Question 47

What is the magnitude of the vector

Question 48

Find the vertex of the parabola

Question 49

Find a polar equation for an ellipse with a focus at (0,0) if the endpoints of its major axis have polar coordinates

Question 50

Find the equation for the conic in standard form. Identify the conic.

Question 51

Write the equation of the conic with focus (2,-3) and directrix y=5 .

Question 52

In three-dimensional space, what are the parametric equations for the line through the points (4,-2,3) and (-1,1,0) ?