gaokao 2022 Q10

gaokao · China · national-A-science 5 marks Conic sections Eccentricity or Asymptote Computation

For the ellipse $C : \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > b > 0 )$, let $A$ be the left vertex. Points $P$ and $Q$ are both on $C$ and symmetric about the $y$-axis. If the product of the slopes of $AP$ and $AQ$ is $\frac { 1 } { 4 }$, then the eccentricity of $C$ is:
A. $\frac { \sqrt { 3 } } { 2 }$
B. $\frac { \sqrt { 2 } } { 2 }$
C. $\frac { 1 } { 2 }$
D. $\frac { 1 } { 3 }$

For the ellipse $C : \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > b > 0 )$, let $A$ be the left vertex. Points $P$ and $Q$ are both on $C$ and symmetric about the $y$-axis. If the product of the slopes of $AP$ and $AQ$ is $\frac { 1 } { 4 }$, then the eccentricity of $C$ is:\\
A. $\frac { \sqrt { 3 } } { 2 }$\\
B. $\frac { \sqrt { 2 } } { 2 }$\\
C. $\frac { 1 } { 2 }$\\
D. $\frac { 1 } { 3 }$

Paper Questions

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