Name: ________________________ Class: ___________________ Date: __________
ID: P
Review Part 1 Parabolas circles ellipses hyperbolas 2016
1.
11. ____ Identify the shape of the graph of the
equation x 2 = 81 − y 2 .
a. ellipse b. parabola c. circle d. hyperbola
2
(y + 9) 2
(x + 9 )
+
=1
82
82
a. ellipse b. circle c. parabola d. hyperbola
2
2
13.
2
(y + 6) 2
(x + 5 )
−
=1
3.
82
42
a. circle b. hyperbola c. parabola d. ellipse
5.
Identify the conic section that the equation
3x 2 + 6x + 3y − 24 = 0 represents.
a. circle b. ellipse c. hyperbola d. parabola
2
4.
2
(y + 6)
(x − 7 )
−
=1
12.
2
8
42
a. hyperbola b. circle c. parabola d. ellipse
2
(y + 3)
(x + 7 )
+
=1
2.
2
2
52
a. parabola b. circle c. ellipse d. hyperbola
14. Find the standard form of the equation of the
specified hyperbola. Center (4,1) Vertex (4,4)
focus (4,6)
(y + 7)
(x − 5 )
−
=1
2
3
42
a. hyperbola b. ellipse c. circle d. parabola
Identify the conic section that the equation
5x 2 − 2xy − 2y 2 − 4x − 3y + 3 = 0 represents.
a. hyperbola b. ellipse c. parabola d. circle
6.
Identify the conic section that the equation
8x 2 − 7xy + y 2 + 5x + 5y + 8 = 0 represents.
a. parabola b. ellipse c. circle d. hyperbola
7.
2
Identify the conic section that the equation
4x 2 − 6xy + y 2 − 7x + 2y + 9 = 0 represents.
a. circle b. hyperbola c. parabola d. ellipse
8.
Identify the conic section that the equation
2x 2 + 2y 2 + 6x − 4y − 8 = 0 represents.
a. ellipse b. parabola c. circle d. hyperbola
2
(y − 4) 2
(x + 8 )
+
=1
9.
92
82
a. circle b. ellipse c. parabola d. hyperbola
10.
2
(y − 1)
(x − 4 )
−
=1
16
9
ÊÁ y − 1 ˆ˜ 2
(x − 4) 2
Ë
¯
−
=1
b.
3
4
ÊÁ y − 1 ˆ˜ 2
(x − 4) 2
Ë
¯
+
=1
c.
9
16
2
ÁÊ y − 1 ˜ˆ
(x − 4) 2
Ë
¯
−
=1
d.
9
16
a.
15. _____ What is the distance between the foci of the
2
x2 y
−
= 1?
hyperbola with equation
10 25
Identify the conic section that the equation
5x 2 + 25x + 5y 2 − 40y − 56 = 0 represents.
a.
a. circle b. ellipse c. hyperbola d. parabola
1
15 b. 2 15 c. 35 d. 2
35
Name: ________________________
ID: P
18. _____ What is the distance between the foci of the
(x − 3) 2 y 2
+
= 1?
ellispe with equation
16
25
16. Find the standard form of the equation of the conic
below.
a.
41 b. 6 c. 3 d. 22 41
19. Given the equation below.
ÊÁ y − 4 ˆ˜ 2 = −8 (x − 3 )
Ë
¯
Find the vertex and focus.
2
(y − 2) 2
(x + 3 )
−
a.
25
4
2
(y − 2) 2
(x + 3 )
+
b.
4
25
2
(y − 2) 2
(x + 3 )
+
c.
25
4
2
(y − 2) 2
(x + 3 )
+
d.
2
5
a. vertex ÁÊË 4,3 ˜ˆ¯
b. vertex ÊÁË 3,4 ˆ˜¯
c. vertex ÊÁË 3,4 ˆ˜¯
d. vertex ÊÁË 4,3 ˆ˜¯
=1
=1
=1
focus ÁÊË 4,1 ˜ˆ¯
focus ÊÁË 1,4 ˆ˜¯
focus ÊÁË 3,2 ˆ˜¯
focus ÊÁË 2,3 ˆ˜¯
20. ____ Identify the shape of the graph of the
equation 9x 2 = 4 − 4y 2 .
a. circle b. hyperbola c. ellipse d. parabola
=1
17. Find the standard form of the equation of the conic
below.
21. Given the equation below.
ÊÁ y − 3 ˆ˜ 2 = 20 (x + 2 )
Ë
¯
Find the:
Vertex_________ Focus_________
equation of the directrix___________
Sketch a complete graph of the conic section.
2
a.
b.
c.
d.
2
(y − 4)
(x + 1 )
−
=1
4
3
ÊÁ y − 4 ˆ˜ 2
(x + 1) 2
Ë
¯
−
=1
9
25
2
ÁÊ y + 1 ˜ˆ
(x − 4) 2
Ë
¯
−
=1
9
16
2
(y − 4) 2
(x + 1 )
−
=1
16
9
2