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- Algebra and trigonometry
- Analytic geometry
- The ellipse
Endpoints of major axis
Endpoints of minor axis
Foci at
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Endpoints of major axis
Endpoints of minor axis
Foci at
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Endpoints of major axis
Endpoints of minor axis
Foci at
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Endpoints of major axis
Endpoints of minor axis
Foci at
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Endpoints of major axis
Endpoints of minor axis
Foci at
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Endpoints of major axis
Endpoints of minor axis
Foci at
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For the following exercises, find the foci for the given ellipses.
Graphical
For the following exercises, graph the given ellipses, noting center, vertices, and foci.
Center
Vertices
Foci
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Center
Vertices
Foci
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Center
Vertices
Focus
Note that this ellipse is a circle. The circle has only one focus, which coincides with the center.
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Center
Vertices
Foci
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Center
Vertices
Foci
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Center
Vertices
Foci
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Center
Vertices
Focus
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For the following exercises, use the given information about the graph of each ellipse to determine its equation.
For the following exercises, given the graph of the ellipse, determine its equation.
Extensions
For the following exercises, find the area of the ellipse. The area of an ellipse is given by the formula
Real-world applications
Find the equation of the ellipse that will just fit inside a box that is four times as wide as it is high. Express in terms of
the height.
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An arch has the shape of a semi-ellipse (the top half of an ellipse). The arch has a height of 8 feet and a span of 20 feet. Find an equation for the ellipse, and use that to find the height to the nearest 0.01 foot of the arch at a distance of 4 feet from the center.
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An arch has the shape of a semi-ellipse. The arch has a height of 12 feet and a span of 40 feet. Find an equation for the ellipse, and use that to find the distance from the center to a point at which the height is 6 feet. Round to the nearest hundredth.
. Distance = 17.32 feet
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A bridge is to be built in the shape of a semi-elliptical arch and is to have a span of 120 feet. The height of the arch at a distance of 40 feet from the center is to be 8 feet. Find the height of the arch at its center.
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A person in a whispering gallery standing at one focus of the ellipse can whisper and be heard by a person standing at the other focus because all the sound waves that reach the ceiling are reflected to the other person. If a whispering gallery has a length of 120 feet, and the foci are located 30 feet from the center, find the height of the ceiling at the center.
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A person is standing 8 feet from the nearest wall in a whispering gallery. If that person is at one focus, and the other focus is 80 feet away, what is the length and height at the center of the gallery?
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Questions & Answers
evolutionary history and relationship of an organism or group of organisms
AI-Robot
the study of living organisms and their interactions with one another and their environments
AI-Robot
cell is the smallest unit of the humanity biologically
Abraham
HOW CAN MAN ORGAN FUNCTION
the diagram of the digestive system
allimentary cannel
Ogenrwot
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
Genetics is the study of heredity
Misack
how does twins formed?
Misack
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
Biology is a branch of Natural science which deals/About living Organism.
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Source:
OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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