Ellipse Questions and Answers

4 An elliptical whispering gallery is 10 m long Anna and Francis find that if they each stand 4 m away from the ends of the gallery at its foci they can hear each other perfectly What is the width of the gallery

In a solar system two comets pass near the sun which is located at the origin Comet E is modeled by all measurements are in astronomical units Part A What are the vertices for the path of Comet E Show your work 4 points x 16 y 1 and Comet H is modeled by 400 144 Part B Which comet travels closer to the sun Give evidence to support your answer 5 points Part C What key feature does the sun represent for both comets Give evidence to support your answer 6 points x 13 y 25 144 1 where

A tunnel is constructed with a semielliptical arch The width of the tunnel is 70 feet and the maximum height at the center of the tunnel is 20 feet What is the height of the tunnel 10 feet from the edge Round your answer to the hundredths place 19 17 feet 16 41 feet 014 01 feet 10 30 feet

A one way road passes under an overpass in the shape of half an ellipse 20 ft high at the center and 20 ft wide Assuming a truck is 16 ft wide what is the tallest truck that can pass under the overpass The tallest truck that can pass under the overpass is ft tall

Drag each sign and value to the correct location on the image Each sign and value can be used more than once but not all signs and values will be used The vertices of an ellipse are at 5 2 and 5 14 and the point 0 6 lies on the ellipse Drag the missing terms and signs to their correct places in the standard form of the equation of this ellipse 6 5 8 2 OD 2 2 VOD 2 1

the following equation of an ellipse Answer Step 3 of 4 Find the endpoints of the major and minor axes of this ellipse 9x 64y 72x 128y 368 0 Enter the coordinates to plot points on the graph Any lines or curves will be drawn once all required points are plotted major axis endpoints Ay 15 10 Enable Zo

Find the equation of the ellipse with the following properties. Express your answer in standard form. Vertices at (-5, -2) and (-5, 12) Minor axis of length 2

Graph the given ellipse. Identify the domain, range, center, vertices, endpoints of the minor axis, and foci in the figure. (x-1)²/4 + (y + 1)²/9 =1 The center of the ellipse is (1,-1). (Type an ordered pair.) The vertices are . (Type ordered pairs. Use a comma to separate answers as needed.)

Consider the following equation of an ellipse. 9x² + 49y² +90x+ 392y + 568 = 0 Step 1 of 4: Rewrite this equation in the standard form of an ellipse. Answer

Consider the following equation of an ellipse. (x+2)^2 /9 + (y-1)^2 /81 =1 Find the center of this ellipse. Answer Enter the coordinates to plot points on the graph. center:

Consider the following equation of an ellipse. (x - 2)²/4+(y + 2)² /16 =1 Step 3 of 3: Find the coordinates of the two foci of this ellipse. Round your answer to two decimal places Enter the coordinates to plot points on the graph.

An arch is in the form of a semi-ellipse, with its major axis as the span. If the span is 80 feet and the height is 30 feet write the standard equation. x²/900+ y²/1600=1 x²/1600+ y²/900=1 x²/6400+ y²/900=1

Find an equation of an ellipse satisfying the given conditions. Foci: (-4, 0) and (4, 0) Length of major axis: 12

Find the equation of the ellipse with the center (6,3), a focus at (3,3), and a vertex at (11,3).

An equation of an ellipse is given. x2/25 + y²/16 = 1 25 16 (a) Find the vertices, foci, and eccentricity of the ellipse.

An elliptical-shaped path surrounds a garden, modeled by (x-22)/225+ (y-26)²/324 =1, where all measurements are in feet. What is the maximum distance between any two persons on the path, and what key feature does this represent? 15 feet; minor axis 18 feet; minor axis 36 feet major axis 225 feet; major axis

An equation of an ellipse is given. (a) Identify the center of the ellipse. (b) Determine the value of a. (c) Determine the value of b. (d) Identify the vertices. (e) Identify the endpoints of the minor axis. (f) Identify the foci. (g) Determine the length of the major axis. (h) Determine the length of the minor axis. (i) Graph the ellipse. Express numbers in exact, simplest form. 9x^2 + 64y^2 = 576

Consider the standard form of the equation x²/25 + y²/36 = 1 The value of a² is, so the y-intercepts are The graph passes through the ordered pairs which are the vertices. The value of b² is, so the x-intercepts are The graph passes through the ordered pairs The value of a² is, so the y-intercepts are The graph passes through the ordered pairs , which are the vertices. The value of b² is, so the x-intercepts are The graph passes through the ordered pairs

Consider the equation of the following (x+8)²/4 conic section: + (y + 6)² = 1. Use Desmos and scratch paper to determine the following characteristics of the conic section: Name of Conic Section: Center. Foci: Eccentricity:

An ellipse has a center at the origin, a vertex along the major axis at (0, 17), and a focus at (0, -8). Which equation represents this ellipse?

Semielliptical Arch Bridge An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 12 meters wide. The center of the arch is 5 meters above the center of the river (see the figure). Write an equation for the ellipse in which the x-axis coincides with the water level and the y-axis passes through the center of the arch. Type the left side of the equation below.

Find an equation of the ellipse that has center (5, 2), a minor axis of length 4, and a vertex at (1,2).

Find an equation of the ellipse that has center (3, 2), a minor axis of length 2, and a vertex at (3,-9).

Find an equation of the ellipse that has center (1,-4), a minor axis of length 4, and a vertex at (-2,-4).

An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 20 meters wide. The center of the arch is 6 meters above the center of the river. Write the equation for this ellipse.

Convince me that the equation of an ellipse that has foci at (2,0) and (-2,0) and a major axis length of 6 has an equation of x^2/9 + y^2/5 = 1

Which of the following could be the equation of an ellipse? (More than one answer may be possible) (x-4)² = 24 (y + 8) (x-4)² + (y + 8)² = 1 (x-4)²/2 - (y + 8)² =1 (x-4)²/2+ (y + 8)²/16 =1

The equation of an ellipse is given below. (x+8)²/169 + (y + 9)²/25 =1 What are the foci of this ellipse? Choose 1 answer: A(-8,-29) and (-8, 11) (28,9) and (-12,9) (-20, -9) and (4, 9) (8.29) and (8, −11)

Given the following equation, what is the location of the center point and what is the length of the semi-minor axis? (x-2)²/81 + (y+1)²/25 =1 (2,-1) and 25 (2,-1) and 5 (-2,1) and 5 (-2,1) and 25

Complete the sentence below. For the ellipse x²/25 + y²/9 = 1, the value of a is , the value of b is , and the major axis is the -axis. For the ellipse x²/25 + y²/9 = 1, the value of a is , the value of b is , and the major axis is the -axis.

Given the ellipse below, determine the coordinates of the two foci. Enter your answers as ordered pairs (x, y) and leave in radical form. (x-1)2/36 + (y+2)2/16 = 1

The vertices of an ellipse are located at (1,4) and (9,4) and its co-vertices are located at (5, 7) and (5, 1). a. Find the center of the ellipse.

An elliptical whispering gallery is 10 m long. Anna and Francis find that if they each stand 4 m away from the ends of the gallery at its foci, they can hear each other perfectly. What is the width of the gallery?

Fill in the blanks below: a. If an ellipse has a major axis length of 8, then its semi-major axis length is_ b. If an ellipse has a minor axis length of 6, then its semi-minor axis length is c. If an ellipse has vertices at (0, 2) and (0, 2) then its major axis length is semi-major axis length is d. If an ellipse has co-vertices at (0, 1) and (0, 1) then its semi-minor axis length is Is this ellipse a horizontal ellipse or a vertical ellipse? e. If a vertical ellipse has a major axis length of 4, its vertices are at f. If a horizontal ellipse has a semi-minor axis length of 3, its co-vertices are at

To determine the break-even point, or the number of units that must be sold so that no profit or loss occurs, an economist uses the formula Px = Cx + F, where P is the selling price per unit, x is the number of units that must be sold to break even, C is the cost to make each unit, and F is the fixed cost. A business analyst has determined that the selling price per unit for a laser printer is $1600. The cost to make one laser printer is $950, and the fixed cost is $211,250. Find the break-even point.

An inspector must select three tests to perform in a certain order on a manufactured part. He has a choice of seven tests. How many ways can he perform three different tests? 5,040 21 210

The plane x + y + 2z = 12 intersects the paraboloid z = x² + y² in an ellipse. Find the points on the ellipse that are nearest to and farthest from the origin. nearest point (x, y, z) = farthest point (x, y, z) =

Write the equation of the ellipse 36x² + 4y² - 360x + 32y + 820 = 0 in standard form (x - h)² p² Where: h = k = P = q= + (y – k)² - q² = 1 M

Bob's backyard is a rectangle 40 meters by 100 meters. He uses this backyard for an exercise area for his dog. He drove two posts into the ground and fastened a rope to each post, passing the rope through the metal ring on his dog's collar. When the dog pulls on the rope while running, its path is an ellipse. If the dog can just reach all four sides of the rectangle, find the equation of the elliptical path. What is the equation of the elliptical path? (Type your answer in standard form.) .....

A system of equations is made up of an ellipse and a hyperbola. Part A: Create the equation of an ellipse centered at the origin, with a horizontal major axis of 8 units and a minor axis of 6 units. Show your work. (3 points) 6 Part B: Create the equation of a hyperbola centered at the origin, with a horizontal transverse axis, vertex at (-7, 0), and asymptotes of y-t-x. Show your work. (4 points) Part C: Determine the domain of each conic section and use it to explain why there is no solution to the system. (3 points)

Which of the following is the equation of the ellipse with a vertical major axis, center at (1, -3), a = 7, and b = 5?

A moon's elliptical orbit around a planet is modeled by the equation 225x² + 900y2 = 202,500, where distance is measured in megameters (Mm). If the planet is the center of the orbit's path, what is the maximum distance between the planet and its moon? 45 Mm 30 Mm 26 Mm 15 Mm

(x+16)²² 400 In a solar system, two comets pass near the sun, which is located at the origin. Comet E is modeled by all measurements are in astronomical units. Part A: What are the vertices for the path of Comet E? Show your work. (4 points) Part B: Which comet travels closer to the sun? Give evidence to support your answer. (5 points) Part C: What key feature does the sun represent for both comets? Give evidence to support your answer. (6 points) 144 = 1 and Comet H is modeled by (x-13)² ² 144 25 = 1, where

Complete the square to determine whether the equation represents an ellipse, parabola, or hyperbola, showing all your work. If the graph is an ellipse, find the center, vertices, and length of the major axis. If it is a hyperbola, find the center, vertices, and asymptotes. If it is a parabola, find the vertex, focus, and directrix. x² + 2y² + 40x + 20y + 434 = 0

Find an equation for the ellipse. Graph the equation. center at (0,0); focus at (0,20); vertex at (0, - 25) Type the left side of the equation of the ellipse.

Find an equation for the ellipse whose vertices are at (2, -9) and (2,3), and focus is at (2,2). Graph the equation.

A tunnel is constructed with a semielliptical arch. The width of the tunnel is 70 feet, and the maximum height at the center of the tunnel is 20 feet. What is the height of the tunnel 10 feet from the edge? Round your answer to the hundredths place. 19.17 feet 16.41 feet 14.01 feet 10.30 feet

Graph the ellipse. Identify the center, vertices, endpoints of the minor axis, and foci. 8x²=160-5y² The center is (). The vertices are (Simplify your answer. Type an ordered pair. Type exact answers for each coordinate, us

An elliptical track has a major axis that is 80 yards long and a minor axis that is 72 yards long. Find an equation for the track if its center is (0, 0) and the major axis is the x-axis.

Let S be the ellipsoid(x/4)² + ( y/3 ) ² + (z/2) ²= 1. Calculate the flux of F = zi over the portion of S where x, y, z ≤ 0 with upward-pointing normal. Hint: Parametrize S using a modified form of spherical coordinates (θ,ϕ).