How to Find Eccentricity?

#Mathematics

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For a conic section, use the definition (e = frac{text{distance from a point on the conic to the focus}}{text{distance from the same point to the directrix}})

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For a circle, (e = 0)

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For an ellipse, (e = frac{c}{a})

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For a parabola, (e = 1)

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For a hyperbola, (e = frac{c}{a})

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For an ellipse or hyperbola, find (a) and (c) from the standard form

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For an ellipse, (c^2 = a^2 - b^2)

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For a hyperbola, (c^2 = a^2 + b^2)

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Substitute (c) and (a) into (e = frac{c}{a})

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For a conic given by focus and directrix, compute the ratio of distances for a point on the curve

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For a conic given by standard equation, identify the type first, then use the matching formula

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