PC PP 9 6 ReviewProblems

Analytic Geometry

Review Problems

Review Problems

Find the focus, directrix, and focal diameter of the parabola, and sketch its graph.

4

7





x













_,

₀

4

7

Review Problems

Find the focus, directrix, and focal diameter of the parabola, and sketch its graph.

Review Problems

Find the focus of the parabola

y

2

_{= 8}

_x

(2, 0)

Review Problems

Find the directrix of the parabola

x

2

_{= 4}

_y

y = –1

Review Problems

Find an equation for the parabola that

has its vertex at the origin and focus

F

(0,

3).

x

2

_{= 12y}

Review Problems

Find an equation for the parabola whose

directrix has

y

-intercept 7.

x

2

_{= –28y}

Review Problems

Find an equation of the parabola whose graph is

shown.

x

2

_{= 16}

_y

Review Problems

A lamp with a parabolic reflector is shown in the

figure. The bulb is placed at the focus, and the focal diameter is 4 cm. Find the diameter d(C, D) of the opening 15 cm from the vertex. ( a = 2, b = 15 )

15 cm

Review Problems

Find the vertices and foci of the ellipse, and

sketch the graph.





10

,

0

 

,

10

,

0





v





8

,

0

  

,

8

,

0



f

Review Problems

Find the intersection points of the pair of ellipses. Sketch the graphs of the pair of equations on the same coordinate axes and label the points of intersection.





3

,

0

  

,

3

,

0

Review Problems

Find the vertices of the ellipse.

(–10, 0) and (10, 0)

Review Problems

foci , major axis 2, minor axis

Review Problems

Find an equation for the ellipse whose graph is shown.

Review Problems

Find an equation for the ellipse that satisfies the given conditions. foci ( 11, 0 ), vertices ( 12, 0 )

Review Problems

Find an equation for the ellipse that satisfies the given conditions. Length of major axis 4, Foci on y-axis,

ellipse passes through the point ( , 0 )

Review Problems

A "sunburst" window above a doorway is constructed in the shape of the top half of an ellipse, as shown in the figure. The window is 30 in tall at its highest point and 60 in wide at the bottom. Find the height of the window 10 in from the center of the base.

Review Problems

Find the vertices, foci, and asymptotes of the hyperbola, and sketch its graph.

Skip

201

2

Review Problems

Find the vertices, foci, and asymptotes of the

hyperbola, and sketch its graph.

Skip

201

2

Review Problems

Find the vertices, foci, and asymptotes of the hyperbola, and sketch its graph.

19

Skip

201

Review Problems

Find the vertices of the hyperbola.

(



4, 0)

Skip

201

2

Review Problems

Find the foci of the hyperbola.

4

x

2

_{– 25}

_y

2

_{= 100}

21

Skip

201

Review Problems

Find the asymptotes of the hyperbola.

9

y

2

_–

_x

2

_{= 1}

Skip

201

2

Review Problems

Find the equation for the hyperbola whose graph is shown. The foci of the hyperbola are F₁(–5, 0) and F₂(5, 0).

23

Skip

201

Review Problems

Find the equation for the hyperbola with foci ( 5, 0) and vertices ( 4, 0).

24

Skip

201

Review Problems

Find the equation for the hyperbola with foci

(0,



8) and asymptotes

Skip

201

2

Review Problems

Find the equation for the hyperbola with the foci ( 10, 0) with transverse axis of length 16.

Skip

201

2

Review Problems

Find the center, foci, and vertices of the ellipse, and determine the lengths of the major and minor axes. Then sketch the graph.

The length of the major

axis is 10, and the length of the minor axis is 6

Review Problems

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

2

9





x















,

0

2

1

v

_













,

0

2

11

f

Review Problems

Find the center, foci, vertices, and asymptotes

of the hyperbola. Then sketch the graph.

The center is (–3, 1), the foci are , the vertices are (–3, 4) and (–3, –2), and the asymptotes are

and

Skip

201

2

Review Problems

Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, or a degenerate conic. If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and

minor axes. If it is a parabola, find the vertex, focus, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. Then sketch the graph of the equation.

Review Problems

Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, or a degenerate conic. If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and

minor axes. If it is a parabola, find the vertex, focus, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. Then sketch the graph of the equation.

The length of major axis is 8,

and the length of minor axis is 6.

Review Problems

Find the lengths of the major and minor axes of the ellipse.

major axis 16, minor axis 4

Review Problems

Find the vertex and focus of the parabola.

–5(

x

+ 8)

2

₌

_y

vertex (–8, 0), focus

Review Problems

Find the center and vertices of the hyperbola.

(

x

– 7)

2

_{– (}

_y

_{+ 6)}

2

_{= 1}

center (7, –6), vertices (8, –6), (6, –6)

Skip

201

2

Review Problems

Find an equation for the conic whose graph is shown.

y

2

_{= 4.8(}

_x

_{+ 2)}

Review Problems

Find an equation for the conic whose graph is shown.

Skip

201

2

Review Problems

Find the center and lengths of the major and

minor axes of the ellipse.

36

y

2

_{+ 9}

_x

2

_{– 108}

_x

_{– 72}

_y

_{+ 36 = 0}

center (6, 1), major axis 12, minor axis 6

Review Problems

Find the vertex and directrix of the parabola.

x

2

_{– 4}

_x

_{– 28}

_y

_{– 248 = 0}

vertex (2, –9), directrix

y

= –16

Review Problems

Sketch the graph.

Skip

201

2

Review Problems

Determine the XY-coordinates of the point if the coordinate axes are rotated through the angle

Review Problems

Determine the

XY

-coordinates of the point

if the coordinate axes are rotated

through the angle

Review Problems

Determine the equation of the conic

in XY-coordinates when the coordinate axes are rotated through the angle

Review Problems

Use the discriminant to determine whether the

graph of the equation

is a parabola, an ellipse, or a hyperbola.

hyperbola

Review Problems

Use a rotation of axes to eliminate the

xy

-term

in the equation

Review Problems

Use a rotation of axes to eliminate the

xy

-term

in the equation

X

2

_{– 4}

_Y

2

_{= 8}

Review Problems

Use a rotation of axes to eliminate the

xy

-term

in the equation

Review Problems

Use a rotation of axes to eliminate the

xy

-term

in the equation

Review Problems

A pair of parametric equations is given. Sketch the curve represented by the parametric equations.

Review Problems

A pair of parametric equations is given. Sketch the curve represented by the parametric equations.

Review Problems

Sketch the curve given by the parametric equations

Review Problems

Use a graphing device to draw the curve represented by the parametric equations.

Review Problems

Use a graphing device to draw the curve

represented by the parametric equations.

Review Problems

Use a graphing device to draw the curve represented by the parametric equations.

ANSWERS

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.graph 18.graph 19.graph 20. 4 7   x       _,0

4 7 8 3  y        8 3 , 0 (2, 0)

y = –1

x 2 _{= 12y}

x 2 _{= –28y}

x 2 _{= 16y}

15 cm

10,0 , 10,0



v f  8,0  , 8,0



3,0

  

, 3,0

(–10, 0) and (10, 0)

foci , major axis 2, minor axis

ANSWERS

21. 22. 23. 24. 25. 26. 27. 28. 29. 30.(-8,8),(-6,8) 31. 32. 33. 34. 35. 36. 37. 38. 39. graph 40.

The length of the major axis is 10, and the length of the minor axis is 6

2 9   x _       ,0

2 1

v f _11₂ ,0_

(–3, 1),

major axis is 8, minor axis is 6.

major axis 16, minor axis 4

vertex (–8, 0), focus

center (7, –6), vertices (8, –6), (6, –6)

y 2 _{= 4.8(x + 2)}

center (6, 1), major axis 12, minor axis 6

ANSWERS

41. 42. 43. 44. 45. 46. 47. 48.Graph 49.Graph 50.Graph 51.Graph 52.Graph 53.Graph 54. 55. 56. 57. 58. 59. 60. hyperbola