Table of Contents
Eccentricity – Formula for Circle, Ellipse, Parabola and Hyperbola
The eccentricity of a curve is a measure of how much the curve deviates from a perfect circle. For a circle, the eccentricity is zero. For an ellipse, the eccentricity is greater than zero, but less than one. For a parabola, the eccentricity is one. For a hyperbola, the eccentricity is greater than one.
Eccentricity Formula
The eccentricity of a curve is a measure of how “stretched out” the curve is. It is defined as the ratio of the distance from the center of the curve to the longest chord to the radius of the curve.
The Eccentricity of Circle
The eccentricity of a circle is a measure of how much the circle deviates from being a perfect circle. Eccentricity is measured in terms of the ratio of the distance from the center of the circle to the circumference of the circle, to the diameter of the circle. The closer this ratio is to 1, the more perfect the circle is. A ratio of greater than 1 indicates that the circle is more eccentric, while a ratio of less than 1 indicates that the circle is more concentric.
The Eccentricity of Parabola
The eccentricity of a parabola is the measure of how “stretched out” the parabola is. The eccentricity is always between 0 and 1.
The Eccentricity of Ellipse
The eccentricity of ellipse is a measure of how “squashed” or “stretched out” the ellipse is. It is defined as the ratio of the distance from the center of the ellipse to the longest axis, to the distance from the center of the ellipse to the shortest axis.
The Eccentricity of Hyperbola
The eccentricity of hyperbola is 1.
The eccentricity of a hyperbola is a measure of how “stretched out” the curve is. The eccentricity is always greater than or equal to zero, and is defined as the ratio of the distance from the center of the curve to the longest distance from the curve. For a hyperbola, this is the difference between the two foci.
Different Values of Eccentricity Make Different Curves
Eccentricity can be a measure of how much an orbit deviates from a perfect circle. The greater the eccentricity, the more elongated the orbit.
There are three types of curves that can be created with different eccentricities:
1. With an eccentricity of 0, the orbit is a perfect circle.
2. With an eccentricity of 1, the orbit is a parabola.
3. With an eccentricity greater than 1, the orbit is an ellipse.
Calculating the Value of Eccentricity (Eccentricity Formula)
The value of eccentricity can be calculated using the following equation:
Eccentricity = (Distance from Center to Foci)/(Distance from Center to Each Point on the Curve)
Questions to be Solved
1. What is the value of x?
2. What is the value of y?
3. What is the value of z?
Eccentricity from Infinity Learn Website
Eccentricity is a measure of how much an orbit deviates from a perfect circle. It is a dimensionless quantity, typically measured in units of radians. An eccentricity of zero means that the orbit is a perfect circle, while an eccentricity of one means that the orbit is a line.
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