MA1310_Week_8_Graphing_Ellipse_Hyperbola_and_ParabolaThis_lab

MA1310: Week 8 Graphing Ellipse, Hyperbola, and Parabola

This lab requires you to:

· Graph ellipses centered at the origin.

· Write equations of ellipses in standard form.

· Graph ellipses not centered at the origin.

· Locate a hyperbola’s vertices and foci.

· Write equations of hyperbolas in standard form.

· Graph hyperbolas centered at the origin.

· Graph parabolas with vertices at the origin.

· Write equations of parabolas in standard form.

· Graph parabolas with vertices not at the origin.

· Solve applied problems involving parabolas.

Answer the following questions to complete this lab:

1. Describe an ellipse in two sentences.

2. Find the standard form of the equation of the ellipse and give the location of its foci.

Standard form of equation of an ellipse with center at the origin, and major and minor axes of lengths 2a and 2b (where a and b are positive, and a2 > b2) is:

The location of foci are at (–c, 0) and (c, 0) where c2 = a2 – b2.

3. Graph the ellipse.

[Hint: In order to graph this ellipse, find the center (h, k) by comparing the given equation with the standard form of equation centered at (h, k). Next, find a and b. Find the vertices (h – a, k) and (h + a, k). Find the foci (h + c, k) and (h – c, k).]

4. A semielliptic archway has a height of 20 feet and a width of 50 feet, as shown in the figure below. Can a truck 14 feet high and 10 feet wide drive under the archway without going into the other lane?

50 ft

20 ft

5. Find the standard form of the equation of the hyperbola whose graph is given below.

6. Find the vertices of the hyperbola.

7. What is a parabola? Describe in two sentences.

8. The giant Arecibo telescope in Puerto Rico has a parabolic dish with a diameter of 300 meters and a depth of 50 meters. (Source: National Astronomy and Ionosphere Center, Arecibo Observatory.)

a. Find an equation in the form that describes a cross section of this dish.

b. If the receiver is located at the focus, how far should it be from the vertex?

(–150, 50)

(150, 50)

Submission Requirements: Answer all the questions included in the lab. You can submit your answers in a Microsoft Word document, or write your answers on paper and then scan and submit the paper. Name the file as InitialName_LastName_Lab8.1_Date.

Evaluation Criteria:

· Did you show the appropriate steps to solve the given problems?

· Did you support your answers with appropriate rationale wherever applicable?

· Were the answers submitted in an organized fashion that was legible and easy to follow?

· Were the answers correct?

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