Let x 2 a 2 + y 2 b 2 = 1 ( b < a ) , be an ellipse with major axis A B and minor axis C D . Let F 1 and F 2 be its two foci, with A , F 1 ,   F 2 ,   B in that order on the segment A B . Suppose ∠ F 1 C B = 90 ° .

Question

Let x 2 a 2 + y 2 b 2 = 1 ( b &#60; a ) , be an ellipse with major axis A B and minor axis C D . Let F 1 and F 2 be its two foci, with A , F 1 , &#160; F 2 , &#160; B in that order on the segment A B . Suppose &#8736; F 1 C B = 90 &#176; . The eccentricity of the ellipse is

Quantrex Academy · Accepted Answer

Correct answer: C. 5 - 1 2

b &#8722; a e &#215; b a = &#8722; 1 &#8658; b 2 = a 2 e &#8658; a 2 1 &#8722; e 2 = a 2 e &#8658; e 2 + e &#8722; 1 = 0 &#8658; e = &#8722; 1 + 5 2

Let x 2 a 2 + y 2 b 2 = 1 ( b < a ) , be an ellipse with major axis A B and minor axis C D . Let F 1 and F 2 be its two foci, with A , F 1 ,   F 2 ,   B in that order on the segment A B . Suppose ∠ F 1 C B = 90 ° . The eccentricity of the ellipse is

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More from Ellipse

Let x 2 a 2 + y 2 b 2 = 1 ( b &#60; a ) , be an ellipse with major axis A B and minor axis C D . Let F 1 and F 2 be its two foci, with A , F 1 , &#160; F 2 , &#160; B in that order on the segment A B . Suppose &#8736; F 1 C B = 90 &#176; . The eccentricity of the ellipse is

Options

Correct answer

Step-by-step solution

More from Ellipse

Let x 2 a 2 + y 2 b 2 = 1 ( b < a ) , be an ellipse with major axis A B and minor axis C D . Let F 1 and F 2 be its two foci, with A , F 1 , F 2 , B in that order on the segment A B . Suppose ∠ F 1 C B = 90 ° . The eccentricity of the ellipse is