Geometry has become extensively important in terms of understanding mathematical figures and structures. Geometry has various kinds of shapes and figures that are studied to solve complex mathematical problems. It is highly important to understand and study these figures properly to be able to do mathematical problems related to geometry, including shapes and figures.

## Circle vs Ellipse

The difference between Circle and Ellipse is that even though both of the figures may seem similar but in a circle, the distance from each point of the circumference to the center is equal, whereas it is not like that in the case of an ellipse where the distance between the center and any point on the circumference is different to each other.

The circle is a geometrical figure which is used to solve problems in mathematics related to geometry. The circle is unique from another geometrical figure as it has the same distance from its center to any particular point made at the circumference of the circle. There can be found plenty of examples of circular figures in daily life such as wheels or bottle caps and so many other instances.

An ellipse is a mathematical figure which is used in geometry to solve geometrical equations related to an ellipse. An ellipse is more of a curve line that is made into a plane on both sides of it. An ellipse may even vary from its size, unlike other geometrical figures.

## Comparison Table Between Circle and Ellipse

Parameters of Comparison | Circle | Ellipse |

Definition | It is a round-shaped mathematical figure with the same distance from any point on the circumference to the center. | It is a mathematical figure where a curve is drawn over a plane both ways to give a flattened circular shape. |

Area | π × r^2 ( r = radius ) | π × a × b |

Definite shape | It has a definite shape of a round figure. | It may vary from the surface towards a more flattened structure of an ellipse. |

Distance from center | It has the same distance from the center to any point in the circumference. | It does not have the same distance from the center. |

Components of figures | One radius at the center. | It has two foci that lie at either end of the ellipse. |

## What is Circle?

A circle is a geometrical figure which is more of a round figured shape and used to solve mathematical equations and problems. It is one of the most common and extensively used mathematical figures, which has its function in geometry.

A circle has a unique feature that all the points in the circumference of a circle are at equal distance to the center. A circle is mostly classified with its shape and the distance from the center. The study of geometrical figures has helped over the development of maths and science over time, and the circle is one of such important figures among the others that has also contributed to the study of mathematics.

A circle also has a definite formula to find its radius and other components that are important for the study of geometry. There are multiple examples of circular figures or objects, even in real life other than mathematical figures. The main principle with which the formation of a circle works is used in the process of creating circular objects in reality.

These applications and principles are used in both mathematics and real life for the processing of these figures, such as the making of wheels in human life.

## What is Ellipse?

An ellipse is a geometrical figure that is a curve line drawn in such a manner above a plane line both ways to give it such a flattened circular shape. It is used to solve mathematical equations or problems related to an ellipse.

An ellipse does not have the same distance with the points from that of its circumference to the center. The curve is drawn in a way that the sum of the distance from two different points, which are known as the foci, while taken from a moving point is constant. An ellipse can be made by a cut produced in a cone by an oblique plane without intersecting the base.

An ellipse may vary in shape and is not confined to a particular type of figure. It can be more or less flattened structure or even somewhat closer to the shape of a circle. An ellipse, unlike a circle, does not have a fixed radius throughout the shape, and it keeps changing.

The most common real-life examples of an ellipse would be the orbits in which the planets are known to revolve around. The astronomical instances can be easily found in real life while studying an ellipse.

## Main Differences Between Circle and Ellipse

- A circle has the same distance from any point on the circumference to the center. Whereas an ellipse does not have the same distance from any point to the center.
- A circle has a fixed shape of a figure even if the viewpoint is moved. While an ellipse may vary in shape, which depends on the distance from each focus.
- A circle has a fixed radius that does not change its position. On the other hand, an ellipse does not have a fixed radius throughout the shape of an ellipse.
- The radius of a circle is at the center, but the two foci of an ellipse lie at either end of an ellipse.
- A circle does not originate from the shape of an ellipse whereas, an ellipse may seem like a flattened circle.

## Conclusion

Mathematical figures are important in the study of maths and science. It helps in the solving of various mathematical equations and problems. Both the circle and ellipse are also such important mathematical figures that have contributed to the study of maths and science and also in the development of scientific attributes, further helping in the experimentation of many such objects.

The examples of a circle and an ellipse are also seen in daily life objects such as wheels and astronomical objects as the orbital paths around planets.

## References

- https://onlinelibrary.wiley.com/doi/abs/10.1901/jeab.1967.10-261
- https://www.sciencedirect.com/science/article/pii/0734189X86902185

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