gaokao 2020 Q8

gaokao · China · national-II-science 5 marks Conic sections Eccentricity or Asymptote Computation
Let $O$ be the origin of coordinates. The line $x = a$ intersects the two asymptotes of the hyperbola $C : \frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > 0 , b > 0 )$ at points $D$ and $E$ respectively. If the area of $\triangle O D E$ is 8, then the minimum value of the focal distance of $C$ is
A. 4
B. 8
C. 16
D. 32
Let $O$ be the origin of coordinates. The line $x = a$ intersects the two asymptotes of the hyperbola $C : \frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > 0 , b > 0 )$ at points $D$ and $E$ respectively. If the area of $\triangle O D E$ is 8, then the minimum value of the focal distance of $C$ is

A. 4

B. 8

C. 16

D. 32