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홈 / 라이브러리 / Gaokao essentials: original practice / AI 플래시카드

In analytic geometry, what is the standard equation and focal length of an ellipse centered at the origin with major axis along the x-axis?

덱 'Gaokao essentials: original practice'의 플래시카드.

정답

$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ ($a > b > 0$), with focal distance $c = \sqrt{a^2 - b^2}$ and foci at $(\pm c, 0)$.

해설

The sum of distances from any point on the ellipse to the two foci is constant and equals $2a$. The eccentricity is $e = c/a \in (0, 1)$.

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