12. Let $F$ be the right focus of the hyperbola $C : \frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > 0 , b > 0 )$, $O$ be the origin. The circle with diameter $O F$ and the circle $x ^ { 2 } + y ^ { 2 } = a ^ { 2 }$ intersect at points $P$ and $Q$. If $| P Q | = | O F |$, then the eccentricity of $C$ is A. $\sqrt { 2 }$ B. $\sqrt { 3 }$ C. 2 D. $\sqrt { 5 }$ II. Fill-in-the-Blank Questions: This section has 4 questions, 5 points each, 20 points total.
D
12. Let $F$ be the right focus of the hyperbola $C : \frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > 0 , b > 0 )$, $O$ be the origin. The circle with diameter $O F$ and the circle $x ^ { 2 } + y ^ { 2 } = a ^ { 2 }$ intersect at points $P$ and $Q$. If $| P Q | = | O F |$, then the eccentricity of $C$ is\\
A. $\sqrt { 2 }$\\
B. $\sqrt { 3 }$\\
C. 2\\
D. $\sqrt { 5 }$
II. Fill-in-the-Blank Questions: This section has 4 questions, 5 points each, 20 points total.\\