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What is the eccentricity $e$ and condition for standard parabola, ellipse, and hyperbola?

デッキ「JEE Main Master Class: Calculus, Mechanics, Coordinate Geometry」の単語カード。

解答

Parabola: $e = 1$; Ellipse: $e = \sqrt{1 - \frac{b^2}{a^2}} < 1$ ($a > b$); Hyperbola: $e = \sqrt{1 + \frac{b^2}{a^2}} > 1$.

解説

Eccentricity measures the degree of deviation of a conic section from circularity ($e = 0$).

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