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Tris Fray Potter
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I know the difference between the two, but I was wondering if parabolas ever became so steep that they turned back into an elliptical shape.
Well observed, indeed. They are different sections of the same double cone, only at different angles:Tris Fray Potter said:I know the difference between the two, but I was wondering if parabolas ever became so steep that they turned back into an elliptical shape.
fresh_42 said:Well observed, indeed. They are different sections of the same double cone, only at different angles:
https://en.wikipedia.org/wiki/Conic_section
Personally, I find the first image in this version better to see what it is about:
https://de.wikipedia.org/wiki/Kegelschnitt
The necessary research is just studying Algebra at the intermediate level, and you will find the most appropriate instruction, textbook discussions, and exercises. Parabola has its own definition using the distance formula. Ellipse has its own but different definition using the distance formula. The definitions and the distance formula are used in deriving equation of each shape. You will want a good instructional textbook on Intermediate Algebra.Tris Fray Potter said:Thank-you! I've only worked with parabolas on a Cartesian plane, so I didn't know that it was part of a cone, and I couldn't decipher anything I found when I did some research!
Regardless of the connections these ellipses have with parabolas, and how they are all conceivably unified under a similar theme, this question must be answerable as a negative. For we know the expression of a parabola, 0 = Ax2 + Bx1 + Cx0 - y. It is clearly a function in the sense that any input x gets assigned to a single output y. No matter how the parameters A,B, or C are tuned, this quality, of the parabola being a function, is unchanged.Tris Fray Potter said:I was wondering if parabolas ever became so steep that they turned back into an elliptical shape.
A parabola is a type of curve that is created by the intersection of a cone and a plane. It has one focus point and is symmetrical. An ellipse, on the other hand, is a closed curve that is formed by the intersection of a cone and a plane. It has two focus points and is not symmetrical.
No, a parabola and an ellipse are two distinct types of curves and cannot be the same. However, a parabola can sometimes resemble an ellipse when viewed from a certain angle or at a certain scale.
A parabola can be recognized by its single focus point and its symmetrical shape. An ellipse can be identified by its two focus points and its elongated, oval shape.
Yes, there are many real-life examples of both parabolas and ellipses. Some common examples of parabolas include the path of a thrown ball, the shape of a satellite dish, and the reflection of light in a concave mirror. Examples of ellipses include the orbits of planets around the sun, the shape of an egg, and the outline of a circular track.
Yes, parabolas and ellipses are used in various scientific fields such as physics, astronomy, and engineering. They are important in understanding the motion of objects, the behavior of light, and the design of structures and machines.