When a plane figure cuts a cone, the conic section is obtained. The conic section is also defined as the curves obtained by the intersection of a cone with a plane. Here, the cone is the conical shape which is also known as the nappes. The eccentricity can be defined as the measure that helps us to find the deviation of the curve based on the circularity of the given shape. Here, the shapes signify the geometrical shapes such as hyperbola, circle, ellipse, and parabola. Depending on the position of the intersection of the plane with the curve, various types of conic sections are formed.
The eccentricity of the conic section can be defined as the total distance from any given point to the focus of the given conic. Focus is one of the major points of a shape which can be defined as the fixed point. The use of eccentricity is to find or determine the curvature of a shape. There is a basic rule which is followed, the rule is: if the curvature of the shape increases the eccentricity decreases. Likewise, when the curvature of the shape decreases, the eccentricity increases. The resultant value of the eccentricity is constant for any conic section. The symbol/letter used to denote the eccentricity is ‘e’. We shall cover the eccentricity of parabola, circle, hyperbola respectively in the coming sections.
Eccentricity of Circle
A circle is a geometrical shape that has edges and vertices on it. The set of points found in a plane that is equidistant from the focus or fixed point is known as the center of the circle. The total distance from the center of the circle to the point of a circle is defined as the radius. The equation of a circle can be easily derived if the center of the circle is situated at the origin. Thus, the eccentricity of a circle is equivalent to zero. Mathematically, e = 0.
Eccentricity of a Parabola
The graph of a quadratic function is known as the parabola. A parabola is also defined as the equation of a curve where the curves are equidistant from the fixed point also known as the focus. The focus of a parabola can be regarded as the a, 0. Similarly, the fixed-line of a parabola is known as the directrix. The standard equation given for a parabola is y.y = 4ax. Hence, the eccentricity of a parabola is equivalent to 1. Mathematically, e ( for a parabola) = 1.
What is Ellipse?
An integral part of a conic section can be defined as the ellipse. Generally, an ellipse resembles the properties of a circle. However, you must not consider an ellipse as a circle because an ellipse more often looks like an oval. The eccentricity of an ellipse is equivalent to less than 1. Mathematically, e < 1. An example of an ellipse is the two-dimensional shape of an egg or the running sports stadium.
Parts of an Ellipse
To recall, an ellipse is considered an integral part of the conics Or conic section. Some parts of an ellipse are, focus, center, major axis, minor axis, eccentricity. The following are the parts of an ellipse.
- The fixed point of an ellipse is known as the focus. A standard ellipse is composed of two focuses also known as foci.
- A-line that joins with the foci of an ellipse is known as the center of an ellipse.
- The length of an axis measuring 2a units is defined as the major axis. Likewise, The length of an axis measuring 2b units is defined as the minor axis.
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