An elliptical riding path is to be built on a rectangular piece of property, as shown below. The rectangular piece of property measures 10 mi by 4 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides.

Q: Sketch the graph and find the foci of the given ellipse 25x squared + 4y squared=100

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Q: In an ellipse, the foci are at (-4, 3) and (4, 3) and one vertex is at (6, 3). How long is the major…

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Q: Write an equation for the given ellipse that satisfies the following conditions. Center at (1,1);…

A: Given Center (1,1) Minor axis vertical with length 16 c=6

Q: Find the coordinates of the foci and vertices, the endpoints of the major axis, minor axis, and the…

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Q: Put the equation of the ellipse in standard form by completing the squqte. 5x2 + 3y2 + 10x + 24y –…

A: This question can be solved using the concept of standard equation of ellipse.

Q: An arch in the form of a semi-ellipse is 50 feet wide at the base and has a height of 16 feet. How…

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Q: A racetrack is in the shape of an ellipse 80 feet long and 60 feet wide. What is the width 32 feet…

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Q: find the length of the major axis and the length of the minor axis of each ellipse. 4x2 + 25y2 = 100

A: To find the length of the major axis and the length of the minor axis of each ellipse.         4x2 +…

Q: A racetrack is in the shape of an ellipse, 100 feet long and 70 feet wide. What is the width 10 feet…

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Q: A certain bridge arch is in the shape of half an ellipse 148 feet wide and 32.1 feet high. At what…

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Q: A racetrack is in the shape of an ellipse 100 feet long and 50 feet wide. What is the width 10 feet…

A: Given that shape of ellipse is 100 feet long and 50 feet wide. Draw a rough sketch showing the given…

Q: Find an equation of the ellipse having a major axis of length 10 and foci at (2, -2) and (2, –8).…

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Q: Make an original question with full solution regarding area of an ellipse. Please include a graph…

A: Here nothing mentioned about which type of question I have to create so I just take a simple…

Q: As viewed from above, a swimming pool has the shape of the ellipse given by

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Q: find the length of the major axis and the length of the minor axis of each ellipse. 2x2 + 7y2 = 28

A: Ellipse is basically a plane curve around 2 focal points such that for all points on the curve, the…

Q: Find the equation in standard form of the ellipse below: 2 1. (1, 0) 1 -1 -2

A: Here is the solution of the given problem.  As we know that the Standard form of an ellipse with…

Q: If the major axis of an ellipse is 26 units in length and the minor axis is 10 units in length,…

A: Major axis of ellipse is a = 26 and minor axis is, b=10Therefore, the eccentricity of ellipse is…

Q: The length of the latus rectum for the ellipse x^2/64 + y^2/16 = 1 is equal to

A: Explanation of the answer is as follows

Q: What is the center, the major axis length, the minor axis length and the equation of the ellipse…

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Q: Find an equation for the ellipse that satisfies the Foci (±3, 0), with a lenght of the minor axis…

A: Given query is to find the equation of ellipse with data given.

Q: A certain bridge arch is in the shape of half an ellipse 134 feet wide and 34.6 feet high. At what…

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Q: Find the standard form of the equation of the ellipse and give the location of its foci. 2) T0 ex:…

A: The given graph is,

Q: Sketch and determine the center, foci and vertices of the ellipse with an equation of x? (y-4)? = 1.…

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Q: Find the DE of an ellipse with the equation: +2²=1

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Q: Draw the ellipse with the equation: 2?2 + ?2 + 4? − 9? = 7

A: Given information: 2?2+?2+4?-9?=7

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A: Let the length of major axis of the ellipse be = 2a The length of minor axis of the ellipse be = 2b…

Q: A certain bridge arch is in the shape of half an ellipse 104 feet wide and 32.3 feet high. At what…

A: Given , a certain bridge is in the shape of half an ellipse which is104 feet wide & 32.3 feet…

Q: Divide both sides of 4x² – 9y? = 36 by 36 and simplify. How does the simplified equation differ from…

A: Given- 4x2-9y2=36 To simplify- The above expression by dividing 36 in both sides and then state how…

Q: Translated to the right 6 units

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Q: Divide both sides of 4x2 - 9y2 = 36 by 36 and simplify. How does the simplified equation differ from…

A: Given: 4x2 - 9y2 = 36

Q: A wire has a shape of an ellipse described by 4r2 + y? = 8. The tempe

A: Given, a wire has a shape of an ellipse described by                                    4x2+y2=8.…

Q: The Statuary Hall in the Capitol Building in Washington, D.C. is a whispering chamber. Its…

A: The given dimensions are, 46 feet wide by 96 feet long as shown in Figure. Here, 96/2 = 48 and 46/2…

Q: Find an equation of the ellipse having the given properties and plot the ellipse.

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: 5. Find the Foci and Vertices of the Ellipse and sketch it, if the Equation is 16x? + 64y? = 256 %3D

A: see the calculation

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Q: Sketch the ellipse, and label the foci, the vertices, and ends of the minor axis. 25(x+4)? + 4(y-1)²…

A: 25x+42+4y-12=100⇒25x+42+4y-12100=1⇒25x+42100+4y-12100=1⇒x+424+y-1225=1⇒x--4222+y-1252=1 Now…

Q: Use the definition of the ellipse to obtain the Cartesian equation.

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Q: Determine whether the graph of the equation is the upper, lower, left, or right half of an ellipse,…

A: Given equation is  x=4525-y2

Q: In an ellipse, what are the two equal lengths that allow you to figure out the location of the foci?

A: In an ellipse, the foci can be find out with the lengths of the major and minor axes to find focu…

Q: The eccentricity of an ellipse with the equation 16x? +9 y + 32 x – 128 = 0 is 0.53 0.66 0.82 0.93

A: We have to find the eccentricity of the ellipse  16x^2+9y^2+32x-128=0

Q: Find the general equation of the ellipse with center at the origin, one focus at (0,-8) and a vertex…

A: Given,            Center is at origin, one focus at 0,-8 and a vertex at 0,6.To find : Equation of…

Q: 1. Olympic Stadium in Montreal, Canada was constructed in the shape of an ellipse with major and…

A: Major axis = 480 mMinor axis = 280 m

Q: An ellipse, centered at the origin, has one vertex at ? = (4, 0) and another vertex at ? =(0, 2).…

A: Let one vertex of the ellipse is at A4,0 and another vertex is at B0,2 and it is centered at the…

Q: In the shown ellipse, the distance from the center to any of the two foci is Select one: O a. 4/3 O…

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

A: Trace the equation

Q: Sketch the ellipse, and label the foci, vertices, and ends of the minor axis. 25x? + y + 25x –36y…

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Q: () and (.0) and 13. Vertices at one

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Q: Draw the ellipse 5(? − 1) 2 + 4(? − 1) 2 = 25, labeling all important information.

A: Consider the ellipse  5x−12+4y−12=25

Q: Find an equation of the ellipse having a major axis of length 12 and foci at (7, 3) and (3, 3). D=0…

A: Given data: The length of major axis is 2a=12. Foci are, (7,3) (3,3)

Q: Suppose a whispering chamber is 480 feet long and 320 feet wide. a. What is the standard form of the…

A: a=480 ,b=320  centre0,0Standard form of ellipse:x-h2a2+y-k2b2=1Foci of Horizontal…

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.