The four defining conditions above can be combined into one condition that depends on a fixed point F i.e. the focus, a line L (the directrix) not containing F and a non-negative real number e (the eccentricity). The corresponding conic section consists of all points whose distance to F equals e times their distance to L.

For 0 < e < 1 we obtain an ellipse,

for e = 1 a parabola, and

for e > 1 a hyperbola.

The distance from the center to the directrix is **a / e**, where **a **is the semi-major axis of the ellipse, or the distance from the center to the top of the hyperbola. The distance from the center to a focus is **ae**.

In the case of a circle, the eccentricity **e** = 0, and the directrix is infinitely far removed from the center.

The eccentricity of a conic section is thus a measure of how far it deviates from being circular.

For a given **a**, the closer **e **is to 1, the smaller is the semi-minor axis.

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- Introduction To Conic Sections
- Eccentricity
- Parameters Of Conic Section
- Parabola
- Forms Of Parabola
- General Equation Of Parabola
- Position Of A Point With Respect To Parabola
- Equation Of A Tangent And Normal At A Point
- Condition Of Tangency
- Point Of Contact Of A Line And A Parabola
- Ellipse
- Ellipse Properties

- Vertical Form Of Ellipse
- General Equation Of Ellipse
- Position Of A Point With Respect To An Ellipse
- Eccentric Angle
- Equations Of Tangent And Normal To An Ellipse
- Condition Of A Line To Touch An Ellipse
- Hyperbola
- Forms Of Hyperbola
- General Equation Of Hyperbola
- Tangent And Normal At A Point On Hyperbola
- Intersection Of A Line And Hyperbola
- Equation Of A Tangent From A Point Outside The Hyperbola

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