Conic Sections
Midpoint and Distance Formula
Class Work
M is the midpoint of A and B. Use the given information to find the missing point.
1. A(4, 2) and B(3, -8), find M
2. A(5, 7) and B( -2, -9), find M
3. A( 2,0) and B(6, -2), find M
4. A( 3, 7) and M(4,-3), find B
5. M(4, -9) and B( -10, 11) find A
6. B(4, 8) and M(-2, 5), find A
7. Find the distance from A(4, 2) to B(3, -8).
8. Find the distance from A(5, 7) to B(-2, -9).
9. Find the distance from A(2,0) to B(6, -2).
10. The distance from A(2, 3) to B(-6, y) is 10, find y.
11. The distance from A(-4, 7) to B(x, 9) is 7, find x.
Homework
M is the midpoint of A and B. Use the given information to find the missing point.
12. A(4, -2) and B(5, 6), find M
13. A(9, 4) and B(-3, -7), find M
14. A(1, 10) and B(6, -2), find M
15. A( 4, 8) and M(4,-3), find B
16. M(8, 7) and B( -10, 11) find A
17. B(-5, 10) and M(-2, 5), find A
18. Find the distance from A(-3, 9) to B(3, -8).
19. Find the distance from A(5, -9) to B(-2, -9).
20. Find the distance from A(-2,10) to B(-6, 0).
21. The distance from A(2, -3) to B(5, y) is 10, find y.
22. The distance from A(4, 6) to B(2x, 9) is 7, find x.
Parabolas
Class Work
What is the vertex of the parabola?
23. 𝑦 = (𝑥 − 2)2 + 4
24. 𝑦 = −3(𝑥 + 5)2 + 5
25. 𝑥 = 5(𝑦 − 7)2 − 6
26. 𝑥 = 2(𝑦 + 4)2 + 9
27. 𝑦 = 2(𝑥 − 7)2 − 9
3
28. 𝑦 = 4 (𝑥)2 + 4
29. 𝑦 = −(𝑥 − 7)2
5
3
30. 𝑥 = (𝑦 + 8)2 − 3
Write the following equations in standard form.
31. 𝑦 = 𝑥 2 + 4𝑥
32. 𝑥 = 𝑦 2 − 8𝑦
33. 𝑦 = 𝑥 2 − 6𝑥 + 8
Geometry - Conics
~1~
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34. 𝑥 = 𝑦 2 + 2𝑦 + 10
35. 𝑦 = 𝑥 2 + 10𝑥 − 12
36. 𝑥 = 𝑦 2 − 8𝑦 + 16
37. 𝑦 = 2𝑥 2 + 12𝑥
38. 𝑥 = 3𝑦 2 − 6𝑦
39. 𝑦 = −4𝑥 2 + 8𝑥 + 6
40. 𝑥 = −6𝑦 2 − 12𝑦 + 15
Graph each of the following. State the direction of the opening. Identify vertex and the focus and
give the equations of the directrix and axis of symmetry.
41. 𝑦 = 2(𝑥 − 4)2 − 3
42. 𝑥 = −3(𝑦 + 2)2 − 6
1
43. 𝑦 = 2 (𝑥 + 6)2 + 5
3
44. 𝑥 = 4 (𝑦 − 5)2 + 7
45. 𝑦 = −(𝑥 − 6)2 − 8
1
46. 𝑥 = − 8 (𝑦 + 5)2
Homework
What is the vertex of the parabola?
47. 𝑦 = (𝑥 + 3)2 + 7
48. 𝑦 = −2(𝑥 + 4)2 + 8
49. 𝑥 = 6(𝑦 − 3)2 − 5
2
50. 𝑥 = 3 (𝑦 + 8)2 − 10
51. 𝑦 = (𝑥 − 12)2 − 11
52. 𝑦 = 2(𝑥 − 3)2
53. 𝑦 = −4(𝑥)2 + 5
2
3
54. 𝑥 = (𝑦)2
Write the following equations in standard form.
55. 𝑦 = 𝑥 2 + 6𝑥
56. 𝑥 = 𝑦 2 − 10𝑦
57. 𝑦 = 𝑥 2 − 4𝑥 + 11
58. 𝑥 = 𝑦 2 + 8𝑦 + 12
59. 𝑦 = 𝑥 2 + 16𝑥 + 49
60. 𝑥 = −𝑦 2 − 8𝑦 + 8
61. 𝑦 = 2𝑥 2 + 8𝑥
62. 𝑥 = 3𝑦 2 − 9𝑦
63. 𝑦 = −5𝑥 2 + 10𝑥 + 16
64. 𝑥 = −2𝑦 2 − 12𝑦 − 30
Graph each of the following. State the direction of the opening. Identify vertex and the focus and
give the equations of the directrix and axis of symmetry.
65. 𝑦 = 8(𝑥 − 2)2 − 4
66. 𝑥 = −5(𝑦 + 1)2 − 7
1
67. 𝑦 = − 4 (𝑥 + 9)2 − 8
Geometry - Conics
~2~
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68. 𝑥 =
69. 𝑦 =
70. 𝑥 =
−3
(𝑦 − 2)2
12
(2𝑥)2
+1
−8
3
(𝑦
8
+ 6)2
Circles
Class Work
What are the center and the radius of the following circles?
71. (𝑥 + 2)2 + (𝑦 − 4)2 = 16
72. (𝑥 − 3)2 + (𝑦 − 7)2 = 25
73. (𝑥)2 + (𝑦 + 8)2 = 1
74. (𝑥 − 7)2 + (𝑦 + 1)2 = 17
75. (𝑥 + 6)2 + (𝑦)2 = 32
Write the standard form of the equation for the given information.
76. center (3,2) radius 6
77. center (-4, -7) radius 8
78. center (5, -9) radius 10
79. center (-8, 0) diameter 14
80. center (4,5) and point on the circle (3, -7)
81. diameter with endpoints (6, 4) and (10, -8)
82. center (4, 9) and tangent to the x-axis
83. 𝑥 2 + 4𝑥 + 𝑦 2 − 8𝑦 = 11
84. 𝑥 2 − 10𝑥 + 𝑦 2 + 2𝑦 = 11
85. 𝑥 2 + 7𝑥 + 𝑦 2 = 11
Homework
What are the center and the radius of the following circles?
86. (𝑥 − 9)2 + (𝑦 + 5)2 = 9
87. (𝑥 + 11)2 + (𝑦 − 8)2 = 64
88. (𝑥 + 13)2 + (𝑦 − 3)2 = 144
89. (𝑥 − 2)2 + (𝑦)2 = 19
90. (𝑥 − 6)2 + (𝑦 − 15)2 = 40
Write the standard form of the equation for the given information.
91. center (-2, -4) radius 9
92. center (-3, 3) radius 11
93. center (5, 8) radius 12
94. center (0 , 8) diameter 16
95. center (-4,6) and point on the circle (-2, -8)
96. diameter with endpoints (5, 14) and (11, -8)
97. center (4, 9) and tangent to the y-axis
98. 𝑥 2 − 2𝑥 + 𝑦 2 + 10𝑦 = 11
99. 𝑥 2 + 12𝑥 + 𝑦 2 + 20𝑦 = 11
100. 4𝑥 2 + 16𝑥 + 4𝑦 2 − 8𝑦 = 12
Geometry - Conics
~3~
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Ellipses
Class Work
Identify the ellipse’s center and foci. State the length of the major and minor axes. Graph the
ellipse.
101.
102.
103.
104.
105.
(x−2)2
4
(x−1)2
9
(x)2
+
25
(x+4)2
16
(x+1)2
6
(𝑦+3)2
+
16
(𝑦−4)2
+
1
(𝑦+5)2
+
=1
=1
36
(𝑦+2)2
+
=1
8
(𝑦−1)2
20
=1
=1
Write the equation of the ellipse in standard form with the following properties.
106. x 2 + 4x + 2y 2 − 8y = 20
107. 4x 2 − 8x + 3y 2 + 18y = 5
108. Center (1,4), a horizontal major axis of 10 and a minor axis of 6.
109. Foci (2,5) and (2,11) with a minor axis of 10
110. Foci (-2,4) and (-6,4) with a major axis of 18
Homework
Identify the ellipse’s center and foci. State the length of the major and minor axes. Graph the
ellipse.
111.
112.
113.
114.
115.
(x+5)2
16
(x−7)2
4
(x−2)2
25
(x)2
+
1
(x+1)2
36
+
+
+
(𝑦−4)2
9
(𝑦+1)2
49
(𝑦)2
64
(𝑦)2
4
+
=1
=1
=1
=1
(𝑦−1)2
18
=1
Write the equation of the ellipse in standard form with the following properties.
116. x 2 + 10x + 2y 2 − 12y = −1
117. 3x 2 − 12x + 4y 2 + 16y = 8
118. Center (-1,2), a vertical major axis of 8 and a minor axis of 4.
119. Foci (3, 5) and (3,11) with a minor axis of 8
120. Foci (-2, 6) and (-8, 6) with a major axis of 14
Hyperbolas
Class Work
Graph each of the following hyperbolas. Write the equations of the asymptotes.
121.
122.
123.
(y+5)2
16
(x−7)2
4
(y−2)2
25
Geometry - Conics
−
−
−
(𝑥−4)2
9
(𝑦+1)2
49
(𝑥)2
64
=1
=1
=1
~4~
NJCTL.org
124.
125.
(x)2
−
1
(y+1)2
36
(𝑦)2
4
−
=1
(𝑥−1)2
18
=1
Write the equation of the hyperbola in standard form.
126. x 2 + 4x − 2y 2 − 8y = 20
127. 3y 2 + 18y−4x 2 − 8x = 1
128.
Opens horizontally, with center (3,7) and asymptotes with slope 𝑚 = ±
129.
Opens vertically, with asymptotes 𝑦 = 2 𝑥 + 8 and 𝑦 = − 2 𝑥 − 4
3
2
5
3
Homework
Graph each of the following hyperbolas. Write the equations of the asymptotes.
130.
131.
132.
133.
134.
(x−2)2
4
(y−1)2
9
(x)2
−
25
(y+4)2
16
(y−6)2
9
−
−
(𝑦+3)2
16
(𝑥−4)2
1
(𝑦+5)2
−
−
=1
=1
36
(𝑥+2)2
8
(𝑥+5)2
30
=1
=1
=1
Write the equation of the hyperbola in standard form.
135. 4y 2 − 24y − 5x 2 + 20x = 4
136. 6y 2 + 36y−x 2 − 14x = 1
3
137.
Opens vertically, with center (-4,1) and asymptotes with slope 𝑚 = ± 7
138.
Opens horizontally, with asymptotes 𝑦 = 9 𝑥 + 10 and 𝑦 = − 9 𝑥 − 14
4
4
Recognizing Conic Sections from the General Form
Class Work
Identify the conic section and state its eccentricity. Write the equation in standard form.
139.
𝑦 2 + 6𝑦 + 𝑥 2 + 10𝑥 = 12
140. 𝑦 2 + 8𝑦 − 𝑥 2 + 12𝑥 = 25
141. 4𝑦 2 + 16𝑦 + 3𝑥 2 − 18𝑥 = 7
142. 𝑦 2 + 2𝑦 − 𝑥 2 + 8𝑥 = 𝑦 2 + 12
143. 2𝑥 2 − 20𝑥 + 2𝑦 2 + 16𝑦 = −6
144. 4𝑥 2 − 24𝑥 − 2𝑦 2 + 8𝑦 = −4
Homework
Identify the conic section and state its eccentricity. Write the equation in standard form.
145.
4𝑦 2 + 8𝑦 + 2𝑥 2 + 12𝑥 = 10
146. 𝑦 2 + 2𝑦 − 𝑥 2 + 8𝑥 = 16
147. 4𝑦 2 + 16𝑦 + 4𝑥 2 − 24𝑥 = 12
148. 𝑦 2 + 2𝑦 + 𝑥 2 + 12𝑥 = 2𝑦 2 + 12
149. 𝑥 2 − 20𝑥 − 2𝑦 2 + 16𝑦 = −6
150. 6𝑥 2 − 24𝑥 + 4𝑦 2 + 8𝑦 = −4
Geometry - Conics
~5~
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Multiple Choice
1. The distance from A(2,y) to B(-1,7) is 5. Find y.
a. 2
b. 3
c. 12
d. A and C
2. M is the midpoint of EF. Find F given E(3,4) and M(5, -2).
a. (4,1)
b. (4,3)
c. (7,-8)
d. (1,10)
3. What is the vertex of the parabola 𝑥 =
−2
(𝑦
3
− 9)2 + 2
a. (9,-2)
b. (-2,2)
c. (2,-2)
d. (2,9)
4. Write the following equations in standard form 𝑥 = 2𝑦 2 + 12𝑦 + 2
a. 𝑥 = 2(𝑥 + 6)2 + 2
b. 𝑥 = 2(𝑥 + 3)2 − 7
c. 𝑥 = 2(𝑥 + 3)2 − 10
d. 𝑥 = 2(𝑥 + 3)2 − 16
5. Identify the focus of 𝑥 =
−2
(𝑦
16
− 3)2 + 2
a. F(0,3)
b. F(4,3)
c. F(2,1)
d. F(2,5)
6. Write the equations of the directrix and axis of symmetry of a parabola with vertex (4,-2) and
focus (4,4).
a. Directrix: y= -8; Axis of Symmetry: x=4
b. Directrix: y= -10; Axis of Symmetry: x=4
c. Directrix: x= -8; Axis of Symmetry: y=4
d. Directrix: x= -10; Axis of Symmetry: y=4
7. Write the equation of the parabola with vertex (4,-2) and focus (4,4).
1
a. 𝑦 = 16 (𝑥 − 4)2 − 2
1
b. 𝑦 = 8 (𝑥 − 4)2 − 2
1
c. 𝑦 = 24 (𝑥 − 4)2 − 2
d. 𝑥 =
1
(𝑦
12
Geometry - Conics
+ 2)2 + 4
~6~
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8. What are the center and the radius of the following circle: (𝑥 − 7)2 + (𝑦 + 6)2 = 4
a. (-7,6); r=4
b. (7,-6); r=16
c. (-7,6); r= 8
d. (7,-6); r= 2
9. Write the equation of the circle with a diameter with endpoints (6, 12) and (17, -8).
a. (x − 11)2 + (y − 6)2 = 521
b. (x − 11)2 + (y + 6)2 = 22.8
c. (x − 11)2 + (y − 2)2 = 521
d. (x − 11)2 + (y − 2)2 = 22.8
10. Identify the ellipse’s center and foci:
(x+4)2
16
+
(𝑦−1)2
36
=1
a. C(-4,1); Foci: (−4 ± √20, 1)
b. C(4,-1); Foci: (4 ± √20, −1)
c. C(-4,1); Foci: (−4,1 ± √20)
d. C(4,-1); Foci: (4,1 ± √20)
11. State the length of the major and minor axes of
(x+4)2
16
+
(𝑦−1)2
36
=1
a. Major: 4; Minor: 6
b. Major: 6; Minor: 4
c. Major: 36; Minor: 16
d. Major: 12; Minor: 8
12. Write the equation in standard form 4y 2 − 24y − 2x 2 + 20x = 22
a.
b.
c.
d.
(y−3)2
2
(y−3)2
2
(y−3)2
27
(y−3)2
27
−
−
−
−
(x−5)2
4
(x+5)2
4
(x−5)2
54
(x+5)2
54
=1
=1
=1
=1
13. What is the slope of the asymptotes for the hyperbola
(y+4)2
16
−
(𝑥+2)2
8
=1
a. 𝑦 = ±2
1
b. 𝑦 = ± 2
c. 𝑦 = ±
√2
2
d. 𝑦 = ±2√2
14. Write the equation in standard form x 2 + 12x + 3y 2 − 12y = −1
a. (𝑥 + 6)2 + 3(𝑦 − 2)2 = 47
b.
(𝑥+6)2
45
+
(𝑦−2)2
15
= 45
2
c. (𝑥 + 6) + 3(𝑦 − 2)2 = 23
d.
(𝑥+6)2
23
+
Geometry - Conics
3(𝑦−2)2
23
= 47
~7~
NJCTL.org
15. Identify the conic section’s eccentricity: 𝑦 2 − 4𝑦 − 𝑥 2 + 6𝑥 = 12
a. e=0
b. 0<e<1
c. e=1
d. e>1
16. Identify the conic section’s eccentricity. 4𝑦 2 + 16𝑦 + 4𝑥 2 − 24𝑥 = 12
a. e=0
b. 0<e<1
c. e=1
d. e>1
Extended Response
1. A parabola has vertex (3, 4) and focus (4, 4)
a. What direction does the parabola open?
b. What are the equations of the axis of symmetry and the directrix?
c. Write the equation of the parabola.
2. Given the general form of a conic section as 𝐴x 2 + Bx + 𝐶𝑦 2 + 𝐷𝑦 + 𝐸 = 0
a. What do A & C tell us about the conic?
b. What is center of the conic if 𝐴 ≠ 0 & 𝐶 ≠ 0?
c. If A, B, C, D are 2 and E is 0, what is eccentricity?
3. Consider a circle and a parabola.
a. At how many points can they intersect?
b. If the circle has equation x 2 + y 2 = 4 and the parabola has equation 𝑦 = 𝑥 2, what
are the point(s) of intersection?
c. If the parabola were reflected over the x-axis, what would be the point(s) of
intersection?
Geometry - Conics
~8~
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Answers
38. X=3(y-1)2 -3
39. Y=-4(x-1)2 +10
40. X=-6(y+1)2 +21
41. Up; v(4,-3); F(4,-2 7/8); Dir: y=-3 1/8;
AOS x=4
42. Left; v(-6,-2) F (-6 ½, -2); dir x=-5 11/12;
AOS y=-2
43. Up v (-6, 5 ½); dir y=4 ½; AOS x=-6
44. right; v(7,5); F(7 1/3, 5) Dir x=6 2/3; AOS
y=5
45. Down; V (6,-8) F(6, -8 ¼) dir y=-7 3/4 ;
AOS x=6
46. Left; v (0,-5); F (-2,-5); dir x=2; AOS y=-5
47. (-3,7)
48. (-4,8)
49. (-5,3)
50. (-10,-8)
51. (12,-11)
52. (3,0)
53. (0,-5)
54. (0,0)
55. Y=(x+3)2 -9
56. X= (Y-5)2 -25
57. Y= (x-2)2 +7
58. X= (y+4)2 -4
59. Y= (x+8)2 -15
60. X=-(Y+4)2 +24
61. Y=2(x+2)2 -8
62. X=3 (y-1.5)2 -3.75
63. Y=-5(x-1)2 +21
64. X=-2(Y+3)2 -12
65. Up v(2,-4) F (2, -3 31/32) Dir y=-4 1/32;
AOS x=2
66. Left; V (-7,-1); F (-7 1/20, -1) Dir x= -6
19/20; AOS y=-1
67. Down; V (-9,-8); F (-9,-9); dir y=-7; AOS
x=-9
1. (3.5, -3)
2. (1.5, -1)
3. (4,-1)
4. (5,-13)
5. (18,-29)
6. (-8,2)
7. 10.05
8. 17.46
9. 4.47
10. -3 or 9
11. -4+/-3√5
12. (4.5, 2)
13. (3, -1.5)
14. (3.5, 4)
15. (4,-14)
16. (26,3)
17. (1,0)
18. 18.03
19. 7
20. 10.77
21. -3 +/-√91
22. 2 +/− √10
23. (2,4)
24. (-5,5)
25. (-6,7)
26. (9,-4)
27. (7,-9)
28. (0,4)
29. (7,0)
30. (-3,-8)
31. Y=(x+2)2 -4
32. S=(y-4)2 -16
33. Y= (x-3)2 -1
34. (y+1)2+9=x
35. Y=(x+5)2 -37
36. X= )y-4)2
37. Y=2(x+3)2-18
Geometry - Conics
~9~
NJCTL.org
68. Left; v (-1,2); F (-2,2); dir x=0; AOS y=2
69. Up; V (0,-8); F (), -7 ¾); dir y=-8 ¼; AOS
x=0
70. Right; V (0,-6); F (2/3, -6) Dir x=-2/3;
AOS y=-6
71. C (-2,4) r=4
72. C (3,7); r=5
73. C (0,-8); r=1
74. C (7,-1); r= √17
2); maj=8; min =4√2
105.
C (-1,1); F1 (-1,4.74); f2 (-1, 2.74);
maj =4√5; min =2√6
106.
75. C (-6,0); r =4√2
76. (x-3)2 + (x-2)2 =36
77. (x+4)2 + (Y+7)2 =64
78. (x-5)2 + (y+9)2 = 100
79. (x+8)2 + y2 =49
80. (x-4)2 + (y-5)2 =145
81. (x-8)2 + (y+2)2 =40
82. (x-4)2 + (y-9)2 =81
83. (x+2)2 + (y-4)2 =31
84. (x-5)2 + (y+1)2 =37
85. (x+3.5)2 + y2 =23.25
86. C (9,-5) r=3
87. C -11, 8) r=8
88. C(-13, 3) r=12
107.
108.
109.
110.
(𝑥+2)2
32
(𝑥−1)2
9
(𝑥−1)2
25
(𝑥−2)2
25
(𝑥+4)2
81
+
+
+
+
+
(𝑦−2)2
16
(𝑦+3)2
12
(𝑦−4)2
9
(𝑦+8)2
34
(𝑦−4)2
37
=1
=1
=1
=1
=1
111.
C (-5,4); F1(-7.65, 4); F2 (-2.35,
4); Maj=8 min =6
112.
C (7,-1); F1 (&, 5.71); F2 (&,7.71); maj=14; min=4
113.
C (2,0); F1 (2, 6.25); F2 (2, 6.25);
Maj=16; min=10
114.
C(0,0); F1 (),3.8); f1 (), -3.87);
maj=4; min=2
115.
C(-1,1); F (3.23, 1); F2 (-5.24, 1);
89. C(2,0) r= √19
90. C (6,15) r=2√10
91. (x+2)2 +(Y+4)2 =81
92. (x+3)2 + (y-3)2 =121
93. (x-5)2 + (y-8)2 =144
94. X2 + (y-8)2 =64
95. (x+4)2 + (y-6)2 =200
96. (x-8)2 + (y-3)2 = 130
97. (x-4)2 + ( y-9)2 =16
98. (x-1)2 + (y+5)2 =37
99. (x+6)2 + (y+10)2 =147
100.
(x+2)2 + (y-1)2 =8
101.
C (2,-3); F1(2,-6.46) F2 (2, .46);
maj=8; min =4
Geometry - Conics
102.
C (1,4); F1 (3.83, 4) F2(-1.83, 4);
maj=6; min=2
103.
C (0,-5); f1 (0,-8.32) F2 (0, -1.68);
maj=12; min=10
104.
C (-4,-2); F1 (-6.83, -2) F2(-1.17, -
maj =12; min =6√2
116.
117.
118.
119.
120.
~10~
(𝑥+5)2
42
(𝑥−2)2
12
(𝑥+1)2
4
(𝑥−3)2
16
(𝑥+5)2
49
+
+
+
+
+
(𝑦−3)2
21
(𝑦+2)2
9
(𝑦−2)2
16
(𝑦−8)2
25
(𝑦−6)2
40
121.
122.
123.
124.
M = +/- 4/3
M= +/- 7/2
M= +/- 5/8
M= +/- 2
125.
M= +/- √2
=1
=1
=1
=1
=1
NJCTL.org
(𝑥+2)2
126.
16
(𝑦+3)2
127.
8
(𝑥−3)2
128.
25
(𝑦−2)2
129.
(𝑦+2)2
−
8
(𝑥+1)2
−
6
(𝑦−7)2
−
4
(𝑥+4)2
+
9
4
M= +/- √2
134.
M = +/- √30/10
5
(𝑦+3)2
136.
6
(𝑥+4)2
−
9
(𝑥+27)2
138.
4
(𝑥+7)2
−
1
(𝑦−1)2
137.
(𝑥−2)2
81
−
=1
=1
=1
49
(𝑦+2)2
16
=1
Circle; x=0; (x+5)2 + (Y+3)2=46
Hyperbola; e>1:
139.
140.
(𝑦+4)2
5
−
141.
(𝑥−6)2
5
=1
50
+
2(𝑦+2)2
25
=1
6
−
(𝑦−2)2
12
1
c. 𝑥 = 4 (𝑦 − 4)2 + 3
=1
(𝑥+3)2
+
(𝑦+1)2
145.
Ellipse; x<e<4;
146.
147.
148.
Hyperbola; e>1 (Y+1)2 –(x-4)2=1
circle; e=0; (x-3)2+ (y+2)2 =16
hyperbola; e>1;
(𝑥+6)2
47
149.
−
(𝑦−1)2
47
16
8
=1
62
−
(𝑦−4)2
Geometry - Conics
31
2.
a. A and C identify the type of conic
𝐵
𝐷
b. (2𝐴 , 2𝐶)
c. e=0
3.
=1
a. 0, 1, or 2 points
b. (-1.25,1.56) and (1.25, 1.56)
c. (-1.25,-1.56) and (1.25, -1.56)
hyperbola; e>1;
(𝑥−1)2
=1
a. Right
b. Axis of symmetry: y=4,
directrix: x=2
Parabola; e=1;
-2
2
2
Circle; e=0; (x-5) + (y+4) =38
Hyperbola; e>1;
(𝑥−3)2
6
1.
y=1/2(x-4)2
142.
143.
144.
(𝑦+1)2
Extended Response Answers
Ellipse; o<e<1;
3(𝑥−3)2
+
Multiple Choice Answers
1. B
2. A
3. D
4. D
5. A
6. A
7. C
8. D
9. C
10. C
11. D
12. D
13. D
14. A
15. D
16. A
=1
133.
−
4
=1
M = +/- 2
M= +/- 3
M+ +/- 6/5
(𝑦−3)2
(𝑥−2)2
=1
130.
131.
132.
135.
150. ellipse; 0<e<4;
=1
=1
~11~
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