Eccentricity of Circle
A circle is a set of points in a plane that are all the same distance from a fixed point known as the “centre”. The distance from the centre to any point on the circle is called the “radius”.
If the distance from the centre to focus is zero or in other way the centre of the circle is at the origin of a cartesian plane, we derive the equation of a circle. This Eccentricity presents a uniform circular shape.
Elements of Circle
- Centre: The fixed point at the middle of the circle, equidistant from all points on the circumference.
- Radius: The distance from the centre to any point on the circle, defining its size.
Eccentricity of Circle Formula
We derive the equation of the circle as follows:
If “r’ is the radius of circle and C (h, k) is the centre of the circle, Then |CQ| = r.
Formula to find the distance is, √[(x –h)2+( y–k)2] = r
Taking Square on both sides, we get the equation of Circle
(x –h)2+( y – k)2 = r2
Thus, the Eccentricity of the circle is zero, i.e.
e = 0
Eccentricity Formula of Circle, Parabola, Ellipse, Hyperbola
Eccentricity is a non-negative real number that describes the shape of a conic section. It measures how much a conic section deviates from being circular. Generally, eccentricity measures the degree to which a conic section differs from a uniform circular shape.
Let’s discuss Eccentricity formula for circle, parabola, ellipse, and hyperbola, along with examples.
Table of Content
- Eccentricity in Geometry
- Eccentricity Formula
- Eccentricity of Circle
- Eccentricity of Parabola
- Eccentricity of Ellipse
- Eccentricity of Hyperbola
- Eccentricity of Conic Sections
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