Name———————————————————————— Lesson
8.6
Date —————————————
Practice B
For use with the lesson “Translate and Classify Conic Sections”
Graph the equation. Identify the important characteristics of the graph.
(x 2 4)2
( y 2 2)2
2.​ }
   
 1 }
​
​ 
   
​ 5 1
16
4
1. x 2 1 ( y 2 3)2 5 9
y
2
2
(x 1 1)2
( y 1 2)2
4.​ }
   
 2 }
​
​ 
   
​ 5 1
25
18
3. (x 2 3)2 5 8( y 1 4)
y
y
2
2
2
2
x
Lesson 8.6
(x 1 3)2
(y 2 4)2
5.​ }
   
 1 }
​
​ 
   
​ 5 1
32
36
x
2
x
2
y
6. (x 2 5)2 1 (y 1 2)2 5 28
y
x
y
2
2
x
2
2
x
Write an equation of the conic section.
7. Circle with a center at (2, 26) and a radius of 4
8. Parabola with vertex (3, 3) and focus at (3, 0)
9. Ellipse with vertices at (22, 21) and (22, 7) and co-vertices at (24, 3) and (0, 3)
10. Hyperbola with vertices at (2, 4) and (8, 4) and foci at (22, 4) and (12, 4)
Identify the line(s) of symmetry for the conic section.
8-62
11. (y 2 2)2 5 16(x 2 6) 12. (x 2 3)2 1 (y 1 4)2 5 48
(x 2 7)2
y2
13.​ }
   
 1 }
​
​ 
 ​ 5 1
81
62
( y 1 5)2
14.​ }
   
​ 2 (x 2 3)2 5 1
24
Algebra 2
Chapter Resource Book
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Name———————————————————————— Lesson
8.6
Date —————————————
Practice B continued
For use with the lesson “Translate and Classify Conic Sections”
Use the discriminant to classify the conic section.
15. 2x 2 1 5x 1 y 1 14 5 0 16. 4x 2 1 4y 2 2 6x 1 8y 2 10 5 0
17. 5x 2 2 5y 2 1 4x 2 3y 1 4 5 0
18. x 2 1 4y 2 2 8x 2 12y 2 2 5 0
Classify the conic section and write its equation in standard form.
Then graph the equation.
19. y 2 1 8x 2 2y 2 15 5 0
y
20. x 2 1 y 2 2 12x 1 2y 1 15 5 0
2
2
x
2
y
22. 9x 2 1 36y 2 1 54x 2 144y 2 99 5 0
y
2
x
2
2
23. x 2 1 10x 2 6y 1 7 5 0
y
x
Lesson 8.6
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
2
x
2
21. x 2 2 9y 2 1 54y 2 90 5 0 y
24. 22x 2 1 5y 2 1 24x 2 20y 2 102 5 0
y
2
2 x
2
2
x
25. Designing a Menu As part of the graphics art department, your job y
is to create various art pieces and graphical models for your
documents. Your newest project is to design a menu that incorporates
the picture of a tree. The equation used to model the tree trunk is
9x 2 2 y 2 1 8y 2 52 5 0. Write this equation in standard form and
then graph the equation.
2
2
x
26. Long Jump A competitor’s first long jump can be modeled by x 2 2 20x 1 20y 5 0
where x and y are measured in feet and the origin marks the start of the jump. Write
the equation in standard form. How far was the first jump?
Algebra 2
Chapter Resource Book
8-63
Lesson 8.6 Translate and
Classify Conic Sections,
continued
y
2
y
6.
x
; center: (5, 22);
}
radius: 2​Ï 7 ​ 
y
2
x
2
4
answers
( y 2 3)2
(x 1 3)2
23. hyperbola; ​ }
   
 2 }
​
​ 
   
​ 5 1
25
16
; center: (23, 4);
vertices: (23, 10), (23, 22);
}
co-vertices: (23 6 4​Ï 2 ​ , 4);
2
foci: (23, 2), (23, 6)
5.
x
4
(x 2 4)2
( y 2 5)2
24. ellipse; }
​  9   
​ 1 }
​  1   
​ 5 1
y
2
x
2
7. (x 2 2)2 1 (y 1 6)2 5 16
8. (x 2 3)2 5 212(y 2 3)
(x 1 2)2
( y 2 3)2
9. ​ }
   
 1 }
​
​ 
   
​ 5 1
4
16
2
2
(x 2 5)
( y 2 4)
}
10. ​ }
   
 
​
2
​ 
   
 
​5 1 11. y 5 2
9
40
12. any line that passes through the point (3, 24)
25. (x 2 16)2 5 216( y 2 16)
15. parabola 16. circle 17. hyperbola
Practice Level B
1.
13. x 5 7, y 5 0 14. x 5 3, y 5 25
; center: (0, 3);
radius: 3
y
18. ellipse
19. parabola; (y 2 1)2 5 28(x 2 2)
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
y
2
2
2
x
4
2.
; center: (4, 2);
vertices: (0, 2), (8, 2);
co-vertices: (4, 0), (4, 4);
}
x foci: (4 6 2​Ï 3 ​ , 2)
y
2
2
x
20. circle; (x 2 6)2 1 (y 1 1)2 5 22
y
2
3.
; vertex: (3, 24);
focus: (3, 22)
y
x
2
2
x
2
( y 2 3)2
x2
21. hyperbola; ​ }  ​2 }
​ 
   
​ 5 1
9
1
y
4.
4
y
2
; center: (21, 22);
}
vertices: (21, 22 6 3​Ï 2 ​)  ;
}
x
​ 43 ​) 
foci: (21, 22 6 Ï
2
2
x
Algebra 2
Chapter Resource Book
A45
answers
Lesson 8.6 Translate and
Classify Conic Sections,
continued
3.
2
}
; center: (3, 24); radius: 3​Ï 2 ​ 
y
x
2
(x 1 3)2
( y 2 2)2
22. ellipse; }
​  36   
​ 1 }
​  9   
​ 5 1
y
4.
4
; center: (4, 27);
}
Ï
​ 26 ​) ;
vertices: (4, 27 6
x
}
​ 38 ​) 
foci: (4, 27 6 Ï
y
8
2
x
2
23. parabola; (x 1 5)2 5 6(y 1 3)
y
5.
2
y
2
2
2 x
( y 2 2)2
(x 2 6)2
24. hyperbola; ​ }
   
 2 }
​
​ 
   
​ 5 1
10
25
6.
; center: (26, 25);
}
vertices: (26, 25 6 3​Ï3 ​)  ;
x
co-vertices:
}
(26 6 Ï
​ 11 ​ , 25);
foci: (26, 29), (26, 21)
; vertex: (8, 23);
y
focus: ​1 8, 2​ }2 ​ 2​
3
3
y
x
3
2
( y 2 4)2
x2
25. }
​ 4  ​2 }
​  36   
​ 5 1
y
8. (x 2 2)2 5 28(y 2 6)
(x 2 6)2
( y 1 1)2
9. ​ }
   
 1 }
​
​ 
   
​ 5 1
16
13
( y 2 2)2
(x 1 3)2
10. }
​  4   
​ 2 }
​  3   
​ 5 1 11. y 5 24
12. any line that passes through (3, 24)
2
13. x 5 4, y 5 27 14. x 5 26, y 5 25
x
2
15. hyperbola 16. hyperbola 17. circle
26. (x 2 10)2 5 220( y 2 5); 20 ft
18. ellipse
19. parabola; (x 2 7)2 5 9( y 1 3)
Practice Level C
1.
y
; vertex: (5, 24);
focus: (1, 24)
y
4
8
x
2
x
4
20. circle; (x 1 5)2 1 ( y 2 6)2 5 21
2.
2
y
2
; center: (2, 25); }
vertices: (2 6 2​Ï5 ​ , 25);
x
(2, 22), (2, 28);
co-vertices: }
​ 11 ​ , 25)
foci: (2 6 Ï
y
2
2 x
A46
Algebra 2
Chapter Resource Book
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
7. (x 1 3)2 1 (y 1 7)2 5 7
x
2