WorksheetsEllipse and Hyperbola Equations
Total questions: 28
Worksheet time: 1hrs 25mins
Name
Class
Date
1.
What is the equation for the focus points on an ELLIPSE?
a)
c2 = a2 + b2
b)
c2 = a2 - b2
c)
1/4d
d)
(x-h)2 + (y-k)2 = r2
2.
The image provided is the equation of a(n)...
a)
circle
b)
ellipse
c)
parabola
d)
hyperbola
3.
What is the center of the shifted ellipse?
a)
(0,0)
b)
(-3,1)
c)
(1,-3)
d)
(3,-1)
4.
Identify the ellipse as horizontal or vertical. Determine the value of a and b.
a)
Horizontal; a=3, b=2
b)
Vertical; a=3, b=2
c)
Horizontal; a=2, b=3
d)
Vertical; a=2, b=3
5.
What is the center of the shifted ellipse?
a)
(0, 0)
b)
(1, 5)
c)
(1, 0)
d)
(0, 1)
6.
What are the coordinates of the vertices of the shifted ellipse?
a)
(1, 5) and (1, -5)
b)
(0, 5) and (0, -5)
c)
(1, 1) and (1, -1)
d)
(0, 1) and (0, -1)
7.
What are the vertices of the shifted ellipse?
a)
(0, 0)
b)
(7, 1) and (-1, 1)
c)
(3, -5) and (3, 7)
d)
(3, 1)
8.
Given a translated ellipse with vertices (-7, -3), (13, - 3) and foci (- 5, -3) , (11 , -3), what are a and b?
a)
a = 10 , b = 6
b)
a = 6 , b = 10
c)
a = 36 , b = 100
d)
a = 100 , b = 36
9.
Given a translated ellipse with vertices (4, 3), (4, - 9) and the length of the minor axis is 8, what are the values of a and b?
a)
a = 6, b = 3
b)
a = 6, b = 4
c)
a = 36, b = 16
d)
a = 4, b = 6
10.
What are the coordinates of the foci of the shifted ellipse?
a)
(-5,1) and (-1,1)
b)
(±√3,0)
c)
(0,1) and (-6,1)
d)
(√3 - 3,1) and (-√3 - 3,1)
11.
Write the equation of the ellipse:
a)
(x-3)²/2 +(y+2)²/5=1
b)
(x-3)²/4 +(y+2)²/25=1
c)
(x+3)²/2 +(y-2)²/5=1
d)
(x+3)²/4 +(y-2)²/25=1
12.
Identify the center, and if the ellipse is vertical or horizontal.
a)
Vertical; (-2,1)
b)
Horizontal; (-2,1)
c)
Vertical; (2,-1)
d)
Horizontal; (2,-1)
13.
Given the endpoints of the major and minor axis, determine a2 and b2
Major: (2, -7) and (2, 11)
Minor: (-5, 3) and (9, 3)
Major: (2, -7) and (2, 11)
Minor: (-5, 3) and (9, 3)
a)
a2=4 and b2=4
b)
a2=81 and b2=49
c)
a2=9 and b2=7
d)
a2=18 and b2=14
14.
See Picture
a)
A
b)
B
c)
C
d)
D
15.
Find the center and a and b values for the following equation:
x2 + 4y2 + 16x - 80y + 320 = 0
x2 + 4y2 + 16x - 80y + 320 = 0
a)
(-8, 10); a = 12, b = 6
b)
(-8, 10); a = 6, b = 12
c)
(8, -10); a = 12, b = 6
d)
(8, -10); a = 6, b = 12
16.
What are the major axis endpoints?
a)
(2, -6) and (2, 4)
b)
(7, -1) and (-3, -1)
c)
(5, -1) and (-1, -1)
d)
(2, 2) and (-2, -4)
17.
Is the hyperbola vertical or horizontal?
a)
Vertical
b)
Horizontal
18.
What is the equation describing the relationship between dimensions and foci of a hyperbola?
a)
c2 = a2 + b2
b)
c2 = a2 - b2
c)
4p
d)
(x-h)2 + (y-k)2 = r2
19.
What are the vertices of the hyperbola?
a)
(0, 5) and (0, -5)
b)
(5, 0) and (-5, 0)
c)
(0, 25) and (-25, 0)
d)
(0, 0) and (0, 5)
20.
What is the center of the hyperbola?
a)
(0, 4)
b)
(4, 0)
c)
(-4, 0)
d)
(0, -4)
21.
What is the value of a2 for the given hyperbola?
a)
1
b)
-2
c)
25
d)
16
22.
What are the vertices of the hyperbola with the equation 8x² - 9y² = 72?
a)
(±2√2, 0)
b)
(±3, 0)
c)
(0, ±3)
d)
(0, ±2√2)
23.
A hyperbola has vertices (±5, 0) and one focus at (6, 0). What is the equation of the hyperbola in standard form?
a)
x²/25 + y²/11 = 1
b)
x²/5 - y²/11 = 1
c)
x²/11- y²/25 = 1
d)
x²/25 - y²/11= 1
24.
Write the standard form of the following equation:
x2 - 4y2 + 6x - 8y = 11
x2 - 4y2 + 6x - 8y = 11
a)
A
b)
B
c)
C
d)
D
25.
Write the standard form of the following equation:
9y2 - 4x2 + 36y + 32x - 64 = 0
9y2 - 4x2 + 36y + 32x - 64 = 0
a)
A
b)
B
c)
C
d)
D
26.
Find the equation of the asymptotes for
4y² -16x ² =64
4y² -16x ² =64
a)
y = ±2x
b)
y = ±½x
27.
What should replace the blue square in the equation?
a)
-8y
b)
-2y
c)
+2y
d)
+8y
28.
-6x2 + 4y2 + 9x + y = -7
a)
Circle
b)
Parabola
c)
Ellipse
d)
Hyperbola
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