Pre-Calc Assignment 5

Name___________________________________

By signing my name above, I certify that I have completed this assignment individually, working independently and not consulting anyone except the instructor.

Instructions for QUIZ 5:

The quiz is worth 100 points. There are 7 problems. QUIZ 5 is based on Sections 7.2 through 7.5 (also located in the print version of the text “College Algebra, 3rd Corrected Edition”). It is open book and open notes. This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone.

You must show your work. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also.

When you have completed the quiz, upload your solutions file to the Quiz 5 assignment in the Assignment folder.

DUE DATE is NLT 11:59pm EDT, Sunday, October 7.

If you have any questions, please contact me by e-mail. Problem 1. Complete the following 2 problems about circles.

For the general equation of a circle shown below, complete the square and write the equation in standard form. Then give the center and radius of the circle.

1) x2 – 10x + 25 + y2 + 4y + 4 = 4

Answer:

Standard Form: _____________________________________________________

Center: ________________________

Radius: _______________________

1

Write the standard form of the equation of the circle with the given center and radius below. 2) Center (0, -6); Radius = 15

Answer:

Standard Form: __________________________________________________

Problem 2. Complete the following 3 problems about ellipses.

Find the standard form of the equation of the ellipse satisfying the given conditions below.

3) Endpoints of major axis: (-11, 1) and (7, 1); endpoints of minor axis: (-2, -2) and (-2, 4)

Answer:

Standard Form: ___________________________________________________

2

On the axes below, identify the coordinates of the vertices and foci of the ellipse whose equation is shown below, and sketch a graph.

4) x 2

81 +

y2 25

= 1

Answer:

Vertices: __________________________________

Foci: ______________________________________

Convert the equation below to the standard form for an ellipse by completing the square on x and y.

5) 16×2 + 25y2 + 32x + 100y – 284 = 0

Answer:

Standard Form: ___________________________________________________

3

Problem 3.

Find the standard form of the equation of the hyperbola whose graph is shown below. 6)

Answer:

Standard Form: ___________________________________________________

Problem 4.

Find the center, vertices, foci and equations of the asymptotes for the hyperbola described by the equation.

7) (x – 3) 2

100 –

(y + 2)2 81

= 1

Answer:

Center: _____________________

Vertices: ________________________

Foci: ___________________________

Equation of Asymptotes: __________________________________________

4

Problem 5.

Find the standard form of the equation of the parabola using the information given.

8) Vertex: (9, -5); Focus: (9, -7)

Answer:

Standard Form: ___________________________________________________

Problem 6.

Solve the following problem.

9) A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 150 feet and a maximum height of 35 feet. Find the height of the arch at 10 feet from its center. Round your answer to 2 decimal points.

Answer: Height of the arch at 10 feet from its center = _________________________________feet.

5

Problem 7.

Find the vertex, focus, and equation of the directrix of the parabola with the given equation and sketch the graph on the axes labeling these 3 quantities.

10) (y + 4)2 = 16(x + 3)

Answer:

Vertex: _____________________

Focus: ________________________

Equation of Directrix: __________________________________________

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