WorksheetsUnit 12 Conic Sections
Total questions: 18
Worksheet time: 48mins
Name
Class
Date
1.
Given the following equation,
x2+5xy+8y2−10x+3y+10=0
What type of conic section is this?
x2+5xy+8y2−10x+3y+10=0
What type of conic section is this?
a)
Ellipse
b)
Circle
c)
Hyperbola
d)
Parabola
2.
Given the following equation,
x2+5xy+8y2−10x+3y+10=0
What is the degree of rotation between 0 degrees and 90 degrees?
x2+5xy+8y2−10x+3y+10=0
What is the degree of rotation between 0 degrees and 90 degrees?
a)
-35.57
b)
54.46
c)
-17.77
d)
72.23
3.
Given the following equation,
4x2+8xy+4y2−10x+3y+10=0
What type of conic section is this?
4x2+8xy+4y2−10x+3y+10=0
What type of conic section is this?
a)
Ellipse
b)
Circle
c)
Hyperbola
d)
Parabola
4.
What is the equation for the foci points on a hyperbola?
a)
c2 = a2 + b2
b)
c2 = a2 - b2
c)
1/4d
d)
(x-h)2 + (y-k)2 = r2
5.
What is the equation for the foci points on an ellipse?
a)
c2 = a2 + b2
b)
c2 = a2 - b2
c)
1/4d
d)
(x-h)2 + (y-k)2 = r2
6.
Write the Cartesian equation for a parabola, given the graph representation.
a)
a
b)
b
c)
c
d)
d
7.
What are the vertices of the hyperbola?
a)
(0, 3) and (0, -3)
b)
(-4, 3) and (-4, -3)
c)
(0, 1) and (0, -1)
d)
(4, 0) and (-4, 0)
8.
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
9.
Find the equation of the asymptotes for
4y² -16x² =64
4y² -16x² =64
a)
y = ±2x
b)
y = ±½x
c)
y = ±4x
d)
y = ±¼x
10.
What is the directrix of the parabolic conic section 8(y + 3) = (x - 4)2?
a)
y = - 3
b)
x= 5
c)
y= - 5
d)
y= 2
11.
What is p in the equation:
-40(x+4) = (y-9)2
-40(x+4) = (y-9)2
a)
p = - 10
b)
p = 10
c)
p = -40
d)
p = 40
12.
What is the focus of the following parabola?
(y + 5)2 = -12 (x - 2)
(y + 5)2 = -12 (x - 2)
a)
(2, - 5)
b)
( -5, 2)
c)
(1 , -5 )
d)
(-1, -5 )
13.
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)
14.
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)
15.
What are the foci of the hyperbola with the equation y²/12 - x²/5 = 1
a)
(0, ±√17)
b)
(±√17, 0)
c)
(0, ±√7)
d)
(±√7, 0)
16.
An ellipse has a vertical major axis length of 50 (major radius is 25), and an eccentricity of 0.96. What is the length of the full minor axis?
a)
7
b)
12
c)
14
d)
24
17.
Find an equation with a focus located at (0, 4), whose eccentricity is ⅔, and whose directrix is located at y=9.
a)
x2/20 + y2/36 = 1
b)
x2/36 + y2/20 = 1
c)
x2/9 + y2/4 = 1
d)
x2/4 + y2/9 = 1
18.
An ellipse has a major radius length of 13, and a focal distance (from the center to the focus) is 5. What is the length of one latus rectum (focal width) in this ellipse?
a)
144/13
b)
288/13
c)
169/12
d)
338/12
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