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parshyaa
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i think there is only one focus of ellipse and we can draw a ellipse with a single focus. please correct my thinking.
Your thinking makes no sense. You may be thinking of a parabola. If you are really thinking of an ellipse, then you just need to study them more.parshyaa said:i think there is only one focus of ellipse and we can draw a ellipse with a single focus. please correct my thinking.
If you spend any time studying the math of the ellipse it is very obvious why it has to focii. It's all there in the math and it's not hard. I'm puzzled by your confusion. Have you used the equation of an ellipse to draw one?parshyaa said:so please explain me why ellipse has two focus
Ah, I see your confusion now. Just keep in mind that it is sometimes true that you can use different forms to describe the same thing but if they are indeed describing the same thing, then they have to be equivalent.parshyaa said:there are two definitions of ellipse one is the sum of the distance of a point from two foci is constant and another one is related to eccentricity. i was confused with the proof of the equation of ellipse using second definition because they have used only one foci and one directrix, which made me confused that why there are two foci, but now i got it. thank you my friends. this is the reason why i love physics forum
The requirement of two foci comes from the definition. The set of points in a plane whose sum of distance from two fixed points are equal. Said better in the first paragraph of this article: https://en.wikipedia.org/wiki/Derivation_of_the_Cartesian_form_for_an_ellipseparshyaa said:i think there is only one focus of ellipse and we can draw a ellipse with a single focus. please correct my thinking.
Now that this topic has be discussed rather well, we can state that the name mfb refers to is "circle".mfb said:How would such an ellipse look like? Did you draw one, and if yes, how?
There are ellipses where both focal points are at the same place, but this special case has a different name which is usually preferred.
An ellipse is a geometric shape that is formed by the intersection of a cone and a plane. The two foci of an ellipse are important for understanding its shape and properties. The foci are located on the major axis of the ellipse, which is the longest diameter of the shape. They are equidistant from the center of the ellipse and help define its shape and symmetry.
The two foci in an ellipse play a crucial role in determining its shape and size. The distance between the two foci, known as the major axis, is a key factor in calculating the eccentricity of the ellipse. The eccentricity is a measure of how elongated or circular the shape is, and is equal to the distance between the foci divided by the length of the major axis.
The two foci are related to the other elements of an ellipse in several ways. They are located on the major axis, which also contains the longest and shortest diameters of the ellipse. The distance from each focus to any point on the ellipse is equal to the sum of the distances from the two foci. This property is known as the focus-directrix property and is used to define an ellipse geometrically.
No, an ellipse can only have two foci. This is a defining characteristic of an ellipse and differentiates it from other geometric shapes, such as a circle or a parabola. If an ellipse were to have more than two foci, it would no longer be considered an ellipse.
The two foci play a crucial role in the motion of an object in an ellipse. An object placed at one focus of an ellipse will follow an elliptical path around the other focus, known as the center of force. This motion is governed by Kepler's laws of planetary motion and is used to explain the orbits of planets and other celestial bodies.