gaokao 2019 Q4

gaokao · China · beijing-science 5 marks Circles Circle Identification and Classification

Given that the eccentricity of the ellipse $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > b > 0 )$ is $\frac { 1 } { 2 }$, then (A) $a ^ { 2 } = 2 b ^ { 2 }$ (B) $3 a ^ { 2 } = 4 b ^ { 2 }$ (C) $a = 2 b$ (D) $3 a = 4 b$

In ancient Greece, people believed that the most beautiful human body has the ratio of the distance from the top of the head to the navel to the distance from the throat to the navel equal to the golden ratio ($\frac { \sqrt { 5 } - 1 } { 2 } \approx 0.618$). The famous ratio of the length from the top of the head to the base of the neck to the length from the base of the neck to the navel is also the golden ratio. If the total height is 105 cm and the length from the top of the head to the base of the neck is 26 cm,

Given that the eccentricity of the ellipse $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > b > 0 )$ is $\frac { 1 } { 2 }$, then
(A) $a ^ { 2 } = 2 b ^ { 2 }$
(B) $3 a ^ { 2 } = 4 b ^ { 2 }$
(C) $a = 2 b$
(D) $3 a = 4 b$

Paper Questions

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