Trig/Math Anal
Name_______________________No_____
HW NO.
SECTIONS
9-1
9-1
9-2
9-3
9-3
9-4 A
9-4 B
9-4
9-5
9-5
9-6 A
9-6 B
9-6
9-8 A
9-8
9-8 B
9-8 C
Review
ASSIGNMENT
Pg. 382/wr 3-27 eoo
Pg. 383/1, 5, 6
Pg. 387/3-13 odd, 18, 19, 24, 29, 34, 36
Pg. 388/21, 22, 32, 33
Pg. 393/15-20 all
Pg. 409/oral 1-5 graph
Pg. 399/1-15 odd graph, 26, 28
Practice Set A
Pg. 404/1-15 odd, 21, 23, 27
Pg. 409/wr 1-9 odd graph, 17
Practice Set B #1-25 odd CTS and graph
Practice Set B #2-26 eoe CTS and name, 27, 28, 29
Pg. 413-14/1, 2, 3, 5, 7, 11, 13, 14
Pg. 414-15/4, 8, 9
Pg. 421/self test 3: 1-5, 7
Pg. 421/problem at top: 9
Practice Set C
Writing Assignment: Explain how a plane and a
double-napped cone intersect to form different conic
sections (include a description of how a circle, ellipse,
parabola and hyperbola are formed).
DUE
√
California (Math Analysis) Standard(s):
5.0 Complete the square to put equations in standard form and graph. Describe the graph of a conic section using
the coefficients of the quadratic equation that represents it. Identify foci, asymptotes and eccentricity from the
equation. Derive a quadratic equation from a geometric description of the conic section.
Test Date (no graphing calculators allowed):
Practice Set A
Using the definition, find the equation of each conic:
1. directrix y=-3, F(0,1)
2. ellipse: F 0,3 , sum=8
3. parabola: directrix x  2, F (4, 1)
4. ellipse: F (4, 0), sum = 12
Find the equation of the ellipse described:
5. center (3,7); one focus (6,7); one vertex (8,7)
6. center (4,-1); one vertex (4,-5); one focus (4,-3.5)
7. vertices are (5,9) and (5,1); one focus is (5,7) 8. center (5,6); the ellipse tangent to both axes
Practice Set B: Complete the Square
2
2
2
2
1. x  18 x  y  6 y  8  0
2. 16 x  25 y  160 x  150 y  225  0
b g
3.
y 2  6x  6 y  3  0
4.
x 2  y 2  6x  8 y  9  0
5.
y 2  12 x  8 y  116  0
6.
8x 2  6 y 2  64 x  72 y  136  0
7.
x 2  y 2  18x  8 y  61  0
8.
25x 2  4 y 2  150x  32 y  61  0
106744462 Page 1
9.
9 x 2  36 y 2  36x  288 y  288  0
10.
x 2  4 x  4 y  12  0
11.
x 2  y 2  18x  20 y  60  0
12.
49 x 2  64 y 2  294 x  512 y  1671  0
13.
x 2  12 y  4 x  52  0
14.
4 x 2  9 y 2  32 x  144 y  604  0
15.
y 2  6 x  16 y  14  0
16.
9 x 2  4 y 2  36x  24 y  36  0
17.
x 2  y 2  8x  4 y  4  0
18.
9 x 2  5y 2  90x  30 y  45  0
19.
y 2  2 x  8 y  20  0
20.
9 x 2  4 y 2  36x  24 y  36  0
21.
4 x 2  y 2  32 x  6 y  37  0
22.
x 2  y 2  14 x  4 y  3  0
23.
x 2  11y  8x  71  0
24.
y 2  8 x  8 y  32  0
25.
4 y 2  x 2  8 y  4 x  16  0
26.
x 2  32 y  12 x  164  0
Using the definition, find the equation of each conic:
28. Parabola, F(-2, 3) directrix y=1
27. Ellipse, F 4,0 , sum = 10
b g
29. Hyperbola, F b
, diff = 4
0,3g
Practice Set C: Analytic Geometry
x2  y2  5
4 y2  x2  4
4x2  y2  0
3. Solve
1. Graph
2. Solve 2
x  3y  5  0
y  x2  1
x  2 y 2  81
4. Write the equation of a parabola with a
5. Identify:
vertical axis passing through the points (1,3),
a. x 2  y  3
(2,10), and (-2,-6).
b. x 2  y 2  3
c. x 2  3  y 2
d. x  y  3
e. 2 x 2  3  y 2
6. Find the area of ABC with vertices A(-6, 2) B(8, -1) and C(-2, -6)
7. Find the center and radius: x 2  y 2  7 x  4 y  6  0
8. Graph y  4  x 2
xy  3
10. Graph 2
4 x  y 2  16
9. Find the center: 5x 2  8 y 2  25x  20 y  5  0
b g
12. Given P(-4, 5) and Q(1, 7), find:
a. PQ
b. Midpoint of PQ
c. X so Q is midpoint of PX
13. From the definition, write the equation of the ellipse with foci (4, 0) and (-4, 0) and sum=10.
x2  y2  9
14. Graph 2
x  y2  1
15. From the definition, write the equation of the parabola with directrix x=4 and focus (2, 0)
11. Graph x  y  1  3
2
16. Graph x  4  y 2
17. Complete the square and graph: y  x 2  6x  7  0
18. Complete the square and put in standard form: 5x 2  9 y 2  30x  18 y  2  0
ANSWERS
HW No. 9-1
Pg 383: 6. mdpt AB=(3,0); mdpt BC=(5,4); mdpt CD=(1,5); mdpt AD=(-1,1);
slope MN=slope PQ=2; slope PN=slope QM = -1/4
106744462 Page 2
18. ( x  2)2  y 2  16
Pg 387-388:
24. ( x  3)2  ( y  3)2  13
HW No. 9-3
Pg 388: 22. ( x  2)2  ( y  2)2  4 Pg 393: 16. x  2;V (2,1); F (2, 32 ); y  12
18. y  2;V (1, 2); F (1, 2); x  3
Pg 409 oral:
1. circle and line; 2
2. circle and line; 0
3. circle and line; 1
4. parabola and line; 2
5. circle and parabola; 2
HW No. 9-8 A
Pg 413-414: 2.  3,8 1,0 14. no sol. Pg 414-415: 4. 5 m , 12 m 8. 5 by 2 5
HW No. 9-8 B
Pg 421 self: 1b. 1
4. (9, 11), (1, 1)
1c. (1.2,3.3)
Practice Set A
1. y  18 x 2  1
7)
5. ( x 253)  ( y16
1
Practice Set B
 x  9  y  3
1.

2
2
2
6 13
13
x2
7

6.
( x  4)2
9.75
 1 , H, x-axis
1)
 ( y16
1
2
 x  5
2.
  y  4  16 , C
5.  y  4
( x 5)2
12
7.
 y  3
2

25
2
6 13
13

3c. (3, 0)
3b. 2
,  6 1313 ,  6 1313 ,  6 1313
3. x  14 ( y  1) 2  3
2
64
2

, 61313 ,  61313 , 61313 ,
y
 16
1
2.
2
64
4.  x  3

5.
2c. (2.8, 1)
2b. 4
5)
 ( y16
1
2
2
 1 , H, x-axis
2
y
 20
1
4.
x2
36
8.
( x 5)2
25
3.  y  3
2
  y  4  36 , C
8.
 12 x  11 , P, left
2

 y  4
4
10.  x  2
2
 4 y  2  ,P, up
6.
 x  4
2

 y  6
2
 1 , H, x-ax
9.
 x  2
25
11.  x  9
2
2

 y  4
36
  y  10  121 , C
2
12.
2
 12 y  4  , P, up
14.
 x  4
2

 y  8
9
16.
 x  2
2

 y  3
4
2
 1, E
2
2
17.  x  4
20.
22.  x  7
2
  y  2  50 , C
2
2

 x  2
4
28.  x  2
2
 1 , H, y-axis
  y  2  16 , C

 4 y  2 
 x  2
18.
2
 x  5
2

 y  3
2
26.  x  6
2

 y  3
 1 , H, x-axis
2
4
Practice Set C
2. (3, 6), (-3, 6), (3, -6), (-3, -6)
21.
2
2
 11 y  5 ,P, up
 32 y  4  , P, up
9
x
2

x

 1, E
2
 1, E
36
24.  y  4
27.
2
45
2
25
y
 1, E
 6 x  13 , P, rt
 x  4  y  3
9
23.  x  4
29.
2
49
15.  y  8
2
16
2
 1, E
 y  4
25
 2 x  2  , P, rt
2
4
2
4
 y  1
 1, E
 1 , H, x-axis
9
 x  3
9
19.  y  4
25.
2
2
8
64
13.  x  2
2
16
2
 x  3
2
6)
 ( y36
1
 6 x  2 , P, rt
2
6
7.  x  9

y
2
 8 x  2 , P, rt
2
1
9
2
1
5
3. (1, 2) and (-2, 1)
4. y  x 2  4 x  2
5a. parabola
5b. hyperbola
5c. circle
5d. line
5e. ellipse
6. 50
7. C(-3.5, 2); r=4.7
9. (-2.5, 1.25) 11. v(-3,1) opens rt
12a. 29
2
2
3
x
12c. (6, 9)
12b.  2 ,6
15. x   41 y 2  3
 y9  1
13. 25
b g
106744462 Page 3
16. v(2,0) opens rt
106744462 Page 4
17. v(3, -2) opens up y-int (0, 7) 18. bx 3g2  by 1g2  1
7.6
4.2
The Distance Formula
d
 x2  x1    y2  y1 
2
Equation of an ellipse having foci
 c,0 and sum of focal radii 2a :
2
x2
a2
The Midpoint Formula

x1  x2
2
, y1 2 y2

Equation of an ellipse having foci
 0, c  and focal radii 2a :
Equation of a circle with center  h, k 
and radius r :
2
2
 x  h   y  k   r 2
x2
b2
Equation of a parabola with vertex
 h, k  and axis of symmetry x  h :
y  a ( x  h) 2  k
y2
x  a( y  k ) 2  h
106744462 Page 5
1
a
2
 by2  1 , where c 2  a 2  b 2 .
Equation of a hyperbola having foci
 0, c  and difference of focal radii 2a :
a2
Equation of a parabola with vertex
 h, k  and axis of symmetry y  k :
2
 ay2  1 , where c 2  a 2  b 2 .
Equation of a hyperbola having foci
 c,0 and difference of focal radii 2a :
x2
a2
Length of the latus rectum 
2
 by2  1 , where c 2  a 2  b 2 .
 bx2  1 , where c 2  a 2  b 2 .
2