Trigonometry-MA1310: Module 5 Vectors and Conic Sections

| August 30, 2017

Question
MA1310: Module 5 Vectors and Conic Sections
Exercise 5.2
Graphing Ellipse, Hyperbola, and Parabola

Answer the following questions to complete this exercise:
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.

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

x2 y2

1
a2 b2

or

x2 y2

1
b2 a2

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

a.
1

(x 2)2 (y 1)2

1 and choose the correct graph from the given graphs:
9
4

MA1310: Module 5 Vectors and Conic Sections
Exercise 5.2
Graphing Ellipse, Hyperbola, and Parabola

b.

c.

d.
2

MA1310: Module 5 Vectors and Conic Sections
Exercise 5.2
Graphing Ellipse, Hyperbola, and Parabola

[Hint: 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 semi-elliptic 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?

20 ft
50 ft

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

6. Find the vertices of the hyperbola.
x2 y2

1
25 49

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

3

MA1310: Module 5 Vectors and Conic Sections
Exercise 5.2
Graphing Ellipse, Hyperbola, and Parabola

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?

y

(–150, 50)

(150, 50)
x

Submission Requirements:
Submit your response in a Microsoft Word document of the following specifications:

Font: Arial; Point 12

Spacing: Double

Evaluation Criteria:

Did you show the steps to solve each problem?

Did you write thorough explanations for the short-answer questions?

Did you accurately choose a problem that fits the criteria for each rule?

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

Were the answers correct?

4

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

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