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Chapter 10 Pre Test



Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 

Find the standard form of the equation of the parabola and determine the coordinates of the focus.
mc001-1.jpg
a.
mc001-2.jpg
b.
mc001-3.jpg
c.
mc001-4.jpg
d.
mc001-5.jpg
e.
mc001-6.jpg
 

 2. 

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin.
directrix:  x = 1
a.
x2 = –4y
b.
y2 = –4x
c.
x2 = 4y
d.
x2 = y
e.
y2 = x
 

 3. 

Find the vertex and focus of the parabola.
mc003-1.jpg
a.
vertex: mc003-2.jpg    focus: (0, 0)
b.
vertex: (0, 0)     focus: mc003-3.jpg
c.
vertex: (0, 0)     focus: mc003-4.jpg
d.
vertex: (0, 0)     focus: mc003-5.jpg
e.
vertex: mc003-6.jpg   focus: (0, 0)
 

 4. 

Find the vertex and focus of the parabola.
mc004-1.jpg
a.
vertex: mc004-2.jpg          focus: mc004-3.jpg
b.
vertex: mc004-4.jpg          focus: mc004-5.jpg
c.
vertex: mc004-6.jpg          focus: mc004-7.jpg
d.
vertex: mc004-8.jpg          focus: mc004-9.jpg
e.
vertex: mc004-10.jpg          focus: mc004-11.jpg
 

 5. 

Find the vertex and directrix of the parabola.
mc005-1.jpg
a.
vertex: mc005-2.jpg          directrix: mc005-3.jpg
b.
vertex: mc005-4.jpg          directrix: mc005-5.jpg
c.
vertex: mc005-6.jpg          directrix: mc005-7.jpg
d.
vertex: mc005-8.jpg          directrix: mc005-9.jpg
e.
vertex: mc005-10.jpg          directrix: mc005-11.jpg
 

 6. 

Give the standard form of the equation of the parabola with the given characteristics.
vertex: (–1, –3)          directrix: mc006-1.jpg
a.
mc006-2.jpg
b.
mc006-3.jpg
c.
mc006-4.jpg
d.
mc006-5.jpg
e.
mc006-6.jpg
 

 7. 

An elliptical stained-glass insert is to be fitted in a
mc007-1.jpg
rectangular opening (see figure). Using the coordinate system shown, find an equation for the ellipse.
mc007-2.jpg
a.
mc007-3.jpg
b.
mc007-4.jpg
c.
mc007-5.jpg
d.
mc007-6.jpg
e.
mc007-7.jpg
 

 8. 

Find the standard form of the equation of the ellipse with the following characteristics.
foci: mc008-1.jpg          major axis of length: 12
a.
mc008-2.jpg
b.
mc008-3.jpg
c.
mc008-4.jpg
d.
mc008-5.jpg
e.
mc008-6.jpg
 

 9. 

Find the center and vertices of the ellipse.
mc009-1.jpg
a.
center: (7, 0)          vertices: (0, –2), (0, 2)
b.
center: (7, 2)          vertices: (–7, –2), (7, 2)
c.
center: (0, 0)          vertices: (0, –7), (0, 7)
d.
center: (0, 0)          vertices: (–7, 0), (7, 0)
e.
center: (0, 0)          vertices: (–2, 0), (2, 0)
 

 10. 

Find the center and foci of the ellipse.
mc010-1.jpg
a.
center: mc010-2.jpg          foci: mc010-3.jpg
b.
center: mc010-4.jpg          foci: mc010-5.jpg
c.
center: mc010-6.jpg          foci: mc010-7.jpg
d.
center: mc010-8.jpg          foci: mc010-9.jpg
e.
center: mc010-10.jpg          foci: mc010-11.jpg
 

 11. 

Identify the conic by writing the equation in standard form.
mc011-1.jpg
a.
mc011-2.jpg; hyperbola
b.
mc011-3.jpg; ellipse
c.
mc011-4.jpg; hyperbola
d.
mc011-5.jpg; hyperbola
e.
mc011-6.jpg; ellipse
 

 12. 

Identify the conic by writing the equation in standard form.
mc012-1.jpg
a.
mc012-2.jpg; ellipse
b.
mc012-3.jpg; circle
c.
mc012-4.jpg; circle
d.
mc012-5.jpg; circle
e.
mc012-6.jpg; ellipse
 

 13. 

Find the center and vertices of the ellipse.
mc013-1.jpg
a.
center: mc013-2.jpg          vertices: mc013-3.jpg
b.
center: mc013-4.jpg          vertices: mc013-5.jpg
c.
center: mc013-6.jpg          vertices: mc013-7.jpg
d.
center: mc013-8.jpg          vertices: mc013-9.jpg
e.
center: mc013-10.jpg          vertices: mc013-11.jpg
 

 14. 

Identify the conic by writing the equation in standard form.
mc014-1.jpg
a.
mc014-2.jpg; ellipse
b.
mc014-3.jpg; ellipse
c.
mc014-4.jpg; circle
d.
mc014-5.jpg; ellipse
e.
mc014-6.jpg; ellipse
 

 15. 

Find the center and vertices of the ellipse.

mc015-1.jpg = 0
a.
center: (3, –8)            vertices: (0, –8), (6, –8)
b.
center: (8, –3)                vertices: (5, –3), (11, –3)
c.
center: (–8, 3)            vertices: (–11, 3), (–5, 3)
d.
center: (–8, 3)            vertices: (–9, 3), (–7, 3)
e.
center: (8, –3)              vertices: (7, –3), (9, –3)
 

 16. 

Find the standard form of the equation of the ellipse with vertices mc016-1.jpg and eccentricity mc016-2.jpg.
a.
mc016-3.jpg
b.
mc016-4.jpg
c.
mc016-5.jpg
d.
mc016-6.jpg
e.
mc016-7.jpg
 

 17. 

Find the standard form of the equation of the hyperbola with the given characteristics.
vertices: mc017-1.jpg          foci: mc017-2.jpg
a.
mc017-3.jpg
b.
mc017-4.jpg
c.
mc017-5.jpg
d.
mc017-6.jpg
e.
mc017-7.jpg
 

 18. 

Find the standard form of the equation of the hyperbola with the given characteristics.
vertices: (–2, –4), (–2, 6)foci: (–2, –5), (–2, 7)
a.
mc018-1.jpg
b.
mc018-2.jpg
c.
mc018-3.jpg
d.
mc018-4.jpg
e.
mc018-5.jpg
 

 19. 

Find the standard form of the equation of the hyperbola with the given characteristics.
vertices: (0, –1), (10, –1)asymptotes: mc019-1.jpg
a.
mc019-2.jpg
b.
mc019-3.jpg
c.
mc019-4.jpg
d.
mc019-5.jpg
e.
mc019-6.jpg
 

 20. 

A small submarine is in a narrow underwater canyon 30 feet above the bottom searching for two sunken ships that are known to be 500 feet apart on the canyon floor. The sonar indicates that one of the wrecks is on the bottom in front of the sub, 475 feet from the nose of the sub, and the other wreck is on the bottom directly behind the sub, 75 feet from the nose. The difference in the distance from the wrecks to the sub is constant on a hyperbola having the wrecks as foci. 

Assume the two wrecks are positioned on a rectangular coordinate system at points with coordinates (-250, 0) and (250, 0) as shown in the figure. Find the x-coordinate of the position of the submarine. (Round to the nearest whole number, if necessary.)

mc020-1.jpg
a.
x = 204
b.
x = 200
c.
x = 38,400
d.
x = 250
e.
x = 150
 



 
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