Describe a circle as an ellipse?

In summary, a circle can be described as an ellipse if its major and minor axes are of equal length and its center is the gravitational center.
  • #1
aisha
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0
Describe a circle as an ellipse??

An ellipse is a stretched circle. Can you describe a circle as an ellipse? If so, what are the foci of the circle?
What are the lengths of the minor and major axis?
Would this circle satisfy the locus definition of an ellipse?

I really don't know how a circle can be described as an ellipse. If it is possible then how will I find the foci and lengths? There are no numbers? What acutally is the locus definition of an ellipse?

Please help me get started I don't know what to do. :cry:
 
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  • #2
Think of a circle as having 2 axis perpendicular to each other (like an ellipse) that both pass through the center. What can be said about their lengths?

what is the equation of an ellipse, where does the length of the axis show up in that equation?
 
  • #3
A circle is a special case of an ellipse where both foci are concentrated at its gravitational center and as a consequence and a characteristic, the length between any point and the foci is always equal.
 
  • #4
What, pray tell, is a "gravitational center" in terms of euclidean geometry? I wouldn't know quite what to tell a student who wrote about the gravitational center of a circle on a geometry test, without some sort of definition :wink:.

Anyways, the sentiment is correct: A circle can be described as an ellipse with major and minor axes of equal length, or equivalently as an ellipse with coincident focii.
 
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  • #5
This is because the only forms that really has a center would be circles an spheres... my definition of a center is a point equally separated from each other points... since we are talking of the circle as an ellipse, I didn’t used the term center. The gravitational center would be the point of "equilibrium” and would be located at a equal distance from each angles…
 
  • #6
Werg22,

If you do not know the proper terminology to use in answering such questions, please do not answer them.

- Warren
 
  • #7
Sorry folks, if I my terminology really is wrong, I was not aware of it and I appologize...
 
  • #8
Werg22 said:
Sorry folks, if I my terminology really is wrong, I was not aware of it and I appologize...


S'Okay. The "centroid" of a figure ( one, two or three dimensional) is the "center of gravity" treating the figure as if had uniform density. I presumed immediately that that was what you meant by "gravitational center".
 
  • #9
It is. I didn't meant to give you fallascious terminology. As for Data Euclid does not equal geometry. Mathematicians such as Euler (center of gravity, several theorem on triangles) and Gauss (hyperbolic and parabolic curves) are also pioneers.
 
  • #10
Certainly true. The geometry of the plane is referred to as Euclidean, though, in reference to his fifth postulate (that noncoincident, parallel lines do not meet).
 
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  • #11
thanks so much everyone :smile:
 

Related to Describe a circle as an ellipse?

What is a circle?

A circle is a geometric shape that is defined as the set of all points in a plane that are equidistant from a given point, called the center. It is a closed shape with no corners or edges, and it has a constant radius, which is the distance from the center to any point on the circle.

What is an ellipse?

An ellipse is a geometric shape that is defined as the set of all points in a plane whose distances from two fixed points, called the foci, have a constant sum. It is a closed, curved shape with two distinct foci and two main axes: the major axis and the minor axis.

How is a circle related to an ellipse?

A circle is a special case of an ellipse where the two foci are located at the same point, making the sum of their distances equal to the circle's diameter. Therefore, a circle can be described as an ellipse with equal major and minor axes.

Why is it important to describe a circle as an ellipse?

Describing a circle as an ellipse allows us to better understand the properties and characteristics of circles. It also helps us to make connections between different geometric shapes and concepts, making it easier to solve problems and create new mathematical equations.

What are some real-life examples of circles being described as ellipses?

One example is the orbit of planets around the sun. While they may appear to be circular, they are actually elliptical orbits due to the gravitational pull of the sun. Another example is the shape of tires on a car, which are actually elliptical to better distribute the weight of the vehicle and provide a smoother ride.

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