gaokao 2015 Q7

gaokao · China · sichuan-arts Conic sections Eccentricity or Asymptote Computation

7. A line passing through the right focus of the hyperbola $x ^ { 2 } - \frac { y ^ { 2 } } { 3 } = 1$ and perpendicular to the $x$-axis intersects the two asymptotes of the hyperbola at points $A$ and $B$. Then $| A B | =$ [Figure]
(A) $\frac { 4 \sqrt { 3 } } { 3 }$
(B) $2 \sqrt { 3 }$
(C) 6
(D) $4 \sqrt { 3 }$

7. A line passing through the right focus of the hyperbola $x ^ { 2 } - \frac { y ^ { 2 } } { 3 } = 1$ and perpendicular to the $x$-axis intersects the two asymptotes of the hyperbola at points $A$ and $B$. Then $| A B | =$\\
\includegraphics[max width=\textwidth, alt={}, center]{2d3697d8-6dcb-4d1f-9701-cbe4cd401b55-1_1194_380_1710_1596}\\
(A) $\frac { 4 \sqrt { 3 } } { 3 }$\\
(B) $2 \sqrt { 3 }$\\
(C) 6\\
(D) $4 \sqrt { 3 }$

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