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Chapter 9 Post Test



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

 1. 

Find the slope of the line with inclination mc001-1.jpg. Round your answer to four decimal places.

mc001-2.jpg
a.
mc001-3.jpg
b.
mc001-4.jpg
c.
mc001-5.jpg
d.
mc001-6.jpg
e.
mc001-7.jpg
 

 2. 

Find the angle mc002-1.jpg (in radians and degrees) between the lines. Round your answer to four decimal places for radians and round your answer to one decimal places for degree.

mc002-2.jpg

mc002-3.jpg
a.
mc002-4.jpg
b.
mc002-5.jpg
c.
mc002-6.jpg
d.
mc002-7.jpg
e.
mc002-8.jpg
 

 3. 

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

 4. 

Find the vertex and focus of the parabola.
mc004-1.jpg
a.
vertex: (0, 0)     focus: mc004-2.jpg
b.
vertex: (0, 0)     focus: mc004-3.jpg
c.
vertex: mc004-4.jpg   focus: (0, 0)
d.
vertex: mc004-5.jpg    focus: (0, 0)
e.
vertex: (0, 0)     focus: mc004-6.jpg
 

 5. 

Give the standard form of the equation of the parabola with the given characteristics.
vertex: (–1, –3)          directrix: mc005-1.jpg
a.
mc005-2.jpg
b.
mc005-3.jpg
c.
mc005-4.jpg
d.
mc005-5.jpg
e.
mc005-6.jpg
 

 6. 

A solar oven uses a parabolic reflector to focus the sun's rays at a point 6 inches from the vertex of the reflector (see figure). Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin.
mc006-1.jpg
                       L = 6 inches
a.
mc006-2.jpg
b.
mc006-3.jpg
c.
mc006-4.jpg
d.
mc006-5.jpg
e.
mc006-6.jpg
 

 7. 

Identify the conic as a circle or an ellipse then find the center.

mc007-1.jpg
a.
Circle
Center: mc007-2.jpg
b.
Ellipse
Center: mc007-3.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. 

Use a graphing utility to graph the conic. Determine the angle mc009-1.jpg through which the axes are rotated.

mc009-2.jpg
a.
mc009-3.jpg, mc009-4.jpg
mc009-5.jpg
d.
mc009-12.jpg, mc009-13.jpg
mc009-14.jpg
b.
mc009-6.jpg, mc009-7.jpg
mc009-8.jpg
e.
mc009-15.jpg, mc009-16.jpg
mc009-17.jpg
c.
mc009-9.jpg, mc009-10.jpg
mc009-11.jpg
 

 10. 

Use the discriminant to classify the graph.

mc010-1.jpg
a.
The graph is a cone.
b.
The graph is a circle.
c.
The graph is a parabola.
d.
The graph is a ellipse.
e.
The graph is a hyperbola.
 

 11. 

Use the Quadratic Formula to solve for mc011-1.jpg.

mc011-2.jpg
a.
mc011-3.jpg
b.
mc011-4.jpg
c.
mc011-5.jpg
d.
mc011-6.jpg
e.
mc011-7.jpg
 

 12. 

Consider the equation.

mc012-1.jpg

Without calculating, explain how to rewrite the equation so that it does not have an mc012-2.jpg-term.

a.
To rewrite the equation mc012-3.jpg  so that it does not have an mc012-4.jpg-term, you can solve for mc012-5.jpg in terms of mc012-6.jpg by completing the square or using the Quadratic Formula.
b.
To rewrite the equation mc012-7.jpg  so that it does not have an mc012-8.jpg-term, you can solve for mc012-9.jpg in terms of mc012-10.jpg by completing the square or using the Quadratic Formula.
c.
To rewrite the equation mc012-11.jpg  so that it has an mc012-12.jpg-term, you can solve for mc012-13.jpg in terms of mc012-14.jpg by taking square root or using the Quadratic Formula.
d.
To rewrite the equation mc012-15.jpg  so that it has an mc012-16.jpg-term, you can solve for mc012-17.jpg in terms of mc012-18.jpg by completing the square or using the Quadratic Formula.
e.
To rewrite the equation mc012-19.jpg  so that it has an mc012-20.jpg-term, you can solve for mc012-21.jpg in terms of mc012-22.jpg by completing the square or using the Quadratic Formula.
 

 13. 

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.

mc013-1.jpg
mc013-2.jpg
a.
mc013-3.jpg
b.
mc013-4.jpg
c.
mc013-5.jpg
d.
mc013-6.jpg
e.
mc013-7.jpg
 

 14. 

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.

mc014-1.jpg
mc014-2.jpg
a.
mc014-3.jpg
b.
mc014-4.jpg
c.
mc014-5.jpg
d.
mc014-6.jpg
e.
mc014-7.jpg
 

 15. 

A projectile is launched at a height of h feet above the ground at an angle of mc015-1.jpg with the horizontal. The initial velocity is mc015-2.jpg feet per second, and the path of the projectile is modeled by the parametric equations
mc015-3.jpg and mc015-4.jpg.
Select the correct graph of the path of a projectile launched from ground level at the value of mc015-5.jpg and mc015-6.jpg

mc015-7.jpg, mc015-8.jpg feet per second
a.

mc015-9.jpg
d.

mc015-12.jpg
b.

mc015-10.jpg
e.

mc015-13.jpg
c.

mc015-11.jpg
 

 16. 

A point in rectangular coordinates is given. Convert the point to polar coordinates.

mc016-1.jpg
a.
mc016-2.jpg
b.
mc016-3.jpg
c.
mc016-4.jpg
d.
mc016-5.jpg
e.
mc016-6.jpg
 

 17. 

Convert the polar equation to rectangular form.

mc017-1.jpg
a.
mc017-2.jpg
b.
mc017-3.jpg
c.
mc017-4.jpg
d.
mc017-5.jpg
e.
mc017-6.jpg
 

 18. 

Select the graph of mc018-1.jpg over the interval. Describe the part of the graph obtained in this case.

mc018-2.jpg
a.

mc018-3.jpg
Lower half of circle
d.

mc018-6.jpg
Lower half of circle
b.

mc018-4.jpg
Lower half of circle
e.

mc018-7.jpg
Lower half of circle
c.

mc018-5.jpg
Lower half of circle
 

 19. 

Select the polar equation of the conic for mc019-1.jpg and identify the conic for the following equation.

mc019-2.jpg
a.
mc019-3.jpg mc019-4.jpg hyperbola
b.
mc019-5.jpgmc019-6.jpg hyperbola
c.
mc019-7.jpgmc019-8.jpg hyperbola
d.
mc019-9.jpgmc019-10.jpg hyperbola
e.
mc019-11.jpg mc019-12.jpg hyperbola
 

 20. 

By using a graphing utility select the correct graph of the polar equation.

mc020-1.jpg
a.
mc020-2.jpgmc020-3.jpg Parabola
d.
mc020-8.jpgmc020-9.jpg Parabola
b.
mc020-4.jpgmc020-5.jpg Parabola
e.
mc020-10.jpgmc020-11.jpg Parabola
c.
mc020-6.jpgmc020-7.jpg Parabola
 



 
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