gaokao 2023 Q11

gaokao · China · national-B-science Conic sections Chord Properties and Midpoint Problems
Let $A$ and $B$ be two points on the hyperbola $x ^ { 2 } - \frac { y ^ { 2 } } { 9 } = 1$. Which of the following four points could be the midpoint of segment $AB$?
A. $(1,1)$
B. $( - 1,2 )$
C. $( 1,3 )$
D. $( - 1 , - 4 )$
Let $A$ and $B$ be two points on the hyperbola $x ^ { 2 } - \frac { y ^ { 2 } } { 9 } = 1$. Which of the following four points could be the midpoint of segment $AB$?\\
A. $(1,1)$\\
B. $( - 1,2 )$\\
C. $( 1,3 )$\\
D. $( - 1 , - 4 )$