Question 1

Match the graph to its equation.
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A) 
B) 
C) 
D)

Accepted Answer

The answer of Match the graph to its equation.
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A) 
B)...

Question 2

Solve the problem.
-A searchlight is shaped like a paraboloid of revolution. If the light source is located 5 feet from the basealong the axis of symmetry and the opening is 8 feet across, how deep should the searchlight be?
A)0.8 ft
B)1.6 ft
C)3.2 ft
D)4 ft

Accepted Answer

The answer of Solve the problem.
-A searchlight is shaped like...

Question 3

Solve the problem.
-An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section,cable runs from the top of one tower down to the roadway, just touching it there, and up again to the topof a second tower. The towers are both 12.25 inches tall and stand 70 inches apart. At some point along theroad from the lowest point of the cable, the cable is 1.96 inches above the roadway. Find the distancebetween that point and the base of the nearest tower.
A)21 in.
B)13.8 in.
C)21.2 in.
D)14.2 in.

Accepted Answer

The correct answer is A because the distance between the point where the cable is 1.96 inches above the roadway and the base of the nearest tower is 21 inches.

Question 4

Solve the problem.
-A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex tothe focus is 25 feet and the distance across the top of the mirror is 62 inches, how deep is the mirror in thecenter?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the problem.
-A reflecting telescope has a...

Question 5

Find the center, foci, and vertices of the ellipse.
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A)center at (0, 0)foci at  vertices at (0, -6), (0, 6)
B)center at (0, 0)foci at  vertices at (-6, 0), (6, 0)
C)center at (0, 0)foci at (0, -6)and (0, 6)vertices at (0, -36), (0, 36)
D)center at (0, 0)foci at (0, 6)and (2, 0)vertices at (0, 36)and (4, 0)

Accepted Answer

The answer of Find the center, foci, and vertices of...

Question 6

Graph the equation.
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A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the equation.
-
A) 
B) 
C) 
D) ...

Question 7

Solve the problem.
-An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section,cable runs from the top of one tower down to the roadway, just touching it there, and up again to the topof a second tower. The towers stand 40 inches apart. At a point between the towers and 12 inches along theroad from the base of one tower, the cable is 0.64 inches above the roadway. Find the height of the towers.
A)4 in.
B)4.5 in.
C)3.5 in.
D)6 in.

Accepted Answer

The parabola is symmetric, so the vertex is at the midpoint between the towers, which is 20 inches from each tower. Using the point (12, 0.64) and the vertex form of a parabola, we can solve for the height of the towers. The equation is y = a(x - 20)^2. Substituting the point (12, 0.64) gives 0.64 = a(12 - 20)^2. Solving for a and using the vertex at (20, h) where h is the height of the towers, we find h = 4 inches.

Question 8

Find an equation for the ellipse described.
-Center at (0, 0); focus at (5, 0); vertex at (6, 0)
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find an equation for the ellipse described.
-Center...

Question 9

Match the graph to its equation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Match the graph to its equation.
-
A) 
B)...

Question 10

Write the word or phrase that best completes each statement or answers the question.
-A spotlight has a parabolic cross section that is 6 ft wide at the opening and 2.5 ft deep at the vertex. Howfar from the vertex is the focus? Round answer to two decimal places.
A)0.90 ft
B)0.52 ft
C)0.21 ft
D)0.26 ft

Accepted Answer

The focus of a parabola is located at a distance of p = (1/4a) from the vertex, where a is the distance from the vertex to the focus. In this case, a = 2.5 ft, so p = (1/4)(2.5 ft) = 0.625 ft.

Question 11

Write the word or phrase that best completes each statement or answers the question.
-A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strikethe surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 8 feetacross at its opening and is 2 feet deep at its center, at what position should the receiver be placed?

Accepted Answer

The answer of Write the word or phrase that best...

Question 12

Find the center, foci, and vertices of the ellipse.
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A)center at (0, 0)foci at  vertices at (0, -6), (0, 6)
B)center at (0, 0)foci at  vertices at (-6, 0), (6, 0)
C)center at (0, 0)foci at (0, -6)and (0, 6)vertices at (0, -36), (0, 36)
D)center at (0, 0)foci at (0, 6)and (4, 0)vertices at (0, 36), (16, 0)

Accepted Answer

The answer of Find the center, foci, and vertices of...

Question 13

Solve the problem.
-A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 158 feet and a maximumheight of 30 feet. Find the height of the arch at 10 feet from its center.
A)29.5 ft
B)0.1 ft
C)1.9 ft
D)8.8 ft

Accepted Answer

The equation of a parabolic arch can be represented as $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex of the parabola. Given the maximum height of the arch is 30 feet, this means $k = 30$. The span of the bridge is 158 feet, so the roots of the parabola are at $x = -79$ and $x = 79$ (since the center of the bridge is the vertex of the parabola, and the span is symmetric about the center). The vertex is thus at $(0, 30)$.To find $a$, we use one of the roots, say $x = 79$, and the fact that at this point $y = 0$ (the height at the end of the bridge is 0):$$0 = a(79)^2 + 30$$$$a = -\frac{30}{79^2}$$To find the height at 10 feet from the center, we substitute $x = 10$ into the equation:$$y = -\frac{30}{79^2}(10)^2 + 30$$$$y = -\frac{30}{79^2} \cdot 100 + 30$$$$y = -\frac{3000}{79^2} + 30$$Calculating the exact value:$$y \approx 29.5$$Therefore, the height of the arch at 10 feet from its center is approximately 29.5 feet.

Question 14

Graph the equation.
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A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the equation.
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A) 
B) 
C) 
D) ...

Question 15

Write the word or phrase that best completes each statement or answers the question.
-A sealed-beam headlight is in the shape of a paraboloid of revolution. The bulb, which is placed at thefocus, is 3 centimeters from the vertex. If the depth is to be 6 centimeters, what is the diameter of theheadlight at its opening?

Accepted Answer

The answer of Write the word or phrase that best...

Question 16

Find the center, foci, and vertices of the ellipse.
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A)center at (0, 0)foci at  vertices at (-7, 0), (7, 0)
B)center at (0, 0)foci at  vertices at (0, -7), (0, 7)
C)center at (0, 0)foci at (-7, 0)and (7, 0)vertices at (-49, 0), (49, 0)
D)center at (0, 0)foci at (0, -4)and (0, 4)vertices at (0, -16), (0, 16)

Accepted Answer

The answer of Find the center, foci, and vertices of...

Question 17

Solve the problem.
-A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 16 inchesacross at its opening and is 5 feet deep, where will the light be concentrated?
A)0.3 in. from the vertex
B)3.2 in. from the vertex
C)1.6 in. from the vertex
D)0.8 in. from the vertex

Accepted Answer

The answer of Solve the problem.
-A reflecting telescope contains a...

Question 18

Graph the equation.
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A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the equation.
-
A) 
B) 
C) 
D) ...

Question 19

Solve the problem.
-An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section,cable runs from the top of one tower down to the roadway, just touching it there, and up again to the topof a second tower. The towers are both 6.25 inches tall and stand 50 inches apart. Find the vertical distancefrom the roadway to the cable at a point on the road 10 inches from the lowest point of the cable.
A)1 in.
B)4 in.
C)1.2 in.
D)0.8 in.

Accepted Answer

The parabola is symmetric about the vertical axis through the lowest point of the cable, so the vertical distance from the roadway to the cable at a point 10 inches from the lowest point of the cable is the same as the vertical distance from the roadway to the cable at a point 10 inches from the lowest point of the cable on the other side of the vertical axis. This distance is half the height of the parabola, which is 1 inch.

Question 20

Find the center, foci, and vertices of the ellipse.
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A)center at (0, 0)foci at  vertices at (-9, 0), (9, 0)
B)center at (0, 0)foci at  vertices at (0, -9), (0, 9)
C)center at (0, 0)foci at (-9, 0)and (9, 0)vertices at (-81, 0), (81, 0)
D)center at (0, 0)foci at (0, -6)and (0, 6)vertices at (0, -36), (0, 36)

Accepted Answer

The answer of Find the center, foci, and vertices of...

Quiz 7: Analytic Geometry

Match the graph to its equation. -

Solve the problem. -A searchlight is shaped like a paraboloid of revolution. If the light source is located 5 feet from the basealong the axis of symmetry and the opening is 8 feet across, how deep should the searchlight be?

Solve the problem. -A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex tothe focus is 25 feet and the distance across the top of the mirror is 62 inches, how deep is the mirror in thecenter?

Find the center, foci, and vertices of the ellipse. -

Graph the equation. -

Find an equation for the ellipse described. -Center at (0, 0) ; focus at (5, 0) ; vertex at (6, 0)

Match the graph to its equation. -

Write the word or phrase that best completes each statement or answers the question. -A spotlight has a parabolic cross section that is 6 ft wide at the opening and 2.5 ft deep at the vertex. Howfar from the vertex is the focus? Round answer to two decimal places.

Find the center, foci, and vertices of the ellipse. -

Solve the problem. -A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 158 feet and a maximumheight of 30 feet. Find the height of the arch at 10 feet from its center.

Graph the equation. -

Find the center, foci, and vertices of the ellipse. -

Solve the problem. -A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 16 inchesacross at its opening and is 5 feet deep, where will the light be concentrated?

Graph the equation. -

Find the center, foci, and vertices of the ellipse. -