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Difference between Circle and Ellipse 

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Difference-between-Circle-and-Ellipse

The difference between a circle and an ellipse is that an ellipse has more individual points at varied distances from the centre than a circle, where all of the points are equally far from the centre. 

A cone’s segments are an ellipse and a circle. The cone is divided into four sections: the parabola, hyperbola, ellipse, and circle. A section created by cutting a cone with a plane is known as a conic section. The cone consists of two sides, an axis, and a base. The angle at which the plane and the cone’s axis cross is used to determine the difference between a circle and an ellipse. Ellipses and circles are both closed curves.

Difference between Circle and Ellipse

Mathematically, understanding the difference between a circle and an ellipse is equally important, as they are the cone’s important segments. The comparison between a circle and a cone is provided below:

 CircleEllipse
DefinitionsA circle is a round plane shape with a circumference made up of points spaced equally apart from the centre, which is the fixed point.An ellipse is a regular oval form that is created when a cone is cut by an oblique plane that does not touch the base, or it can be traced by a point travelling in a plane so that the sum of its distances from two other points (the foci) is constant.
VariationsCircles never vary in shape; they have the same shape, even when the view is changed.Ellipses vary in shape and may even go from very broad to almost flat, depending on how far away the foci are from each other.
Radius consistencyIt has a constant radiusIt does not have a constant radius
Main componentsCircle has one radius, which lies at the center
Ellipse has two foci, which are on either ends
Areaπ × r^2Where ‘r’ is the radius of the circle.
π × a × bWhere ‘a’ is length of the Semi-major Axis, and ‘b’ is the length of the Semi-minor Axis.
Standard equations(x-a)^2 + (y-b)^2 = r^2x^2/a^2 + y^2/b^2 = 1
ResemblanceThe special shapes that give rise to all other shapes are circles.Ellipses can also appear as bounded cases of perspective projection and as images of a circle under parallel projection.

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Circle

In basic terms, a circle is a line that creates a closed loop. The collection of points in a circle have equal distances from the centre. There is an exterior and an interior to this closed curve. When the plane crosses the right circular cone perpendicular to the cone axis, it is achieved. A disc, which is likewise obtained in the same manner as a circle, is a three-dimensional figure, meaning that the interior of the circle is also included in the disc. A circle is a two-dimensional figure. For a circle, the eccentricity is zero.

The terminologies used in circle are: 

Arc: Any connected segment of a circle is called an arc.

Centre: The point on the circle that is halfway between the other points.

Radius: Half the circumference of a circle, or the length of a line segment that connects the circle’s centre to any point on the circle.

Diameter: Diameter can refer to either the length of a line segment, which is the greatest distance between any two points on the circle, or to a line segment whose endpoints are on the circle and which passes through the centre. It is the longest chord, which is a particular case of a chord that doubles the radius.

Circumference: The distance made in a single circle circuit.

Chord: A chord is a segment of a line whose ends are on a circle.

Tangent: A coplanar straight line that touches the circle just once is called a tangent.

Semicircle: A semicircle is an area that is enclosed by a diameter and an arc that runs between the ends of the diameter. It is the greatest circle segment, and thus a special case of a circular segment.

Circular Sector: A region enclosed by two radii and an arc between them is known as a circular sector.

Also Read: What is the Difference Between Prime and Composite Numbers

Ellipse

When the plane passes through the cone orthogonally along its axis, an ellipse is formed. An ellipse is a unique circle. The distance between two fixed points (foci) and the locus of all points on the plane in an ellipse adds up to the same constant every time.

The terminologies used in ellipse are: 

Focus: The main and minor radii are used to describe the distance from the centre.

Eccentricity: The flattening factor is used to express the eccentricity of the ellipse, which is generally represented by either e or ε.

Dirctrix: The directrix is a line that runs parallel to the minor axis and is connected to every focus.

Latus rectum: An ellipse’s latus rectum is the section of its chords that passes through one of its foci and is perpendicular to the major axis.

Major/ Minor axis: The longest and shortest diameters of an ellipse are its major and minor axis. The two generator lines added together equal the length of the major axis.

Semi-Major/ Semi-Minor axis: The distance on the ellipse between the centre and the closest and furthest point is known as the semi-major/semi-minor axis. The major/minor axis is in half.

Chords: An ellipse’s collinear midpoints are those of a set of parallel chords.

Circumference: A crucial component of an ellipse, it is related to the eccentricity and the length of the semi-major axis.

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FAQs

Is every circle an ellipse?

Yes, an ellipse is a circle. The collection of all points such that the total distance between those locations and two fixed points (referred to as the ellipse’s foci) is constant is the formal definition of an ellipse.

What is the similarity between a circle and an ellipse?

Conic sections include shapes like circles and ellipses. An ellipse with the same radius at every point is special cased as a circle. An ellipse is formed by extending a circle in either the x or y direction.

What is the area of a circle?

The area of a circle is,
π × r^2
Where ‘r’ is the radius of the circle.

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