gaokao 2019 Q10

gaokao · China · national-III-arts Conic sections Triangle or Quadrilateral Area and Perimeter with Foci

10. Let $F$ be a focus of the hyperbola $C : \frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 5 } = 1$ . Point $P$ is on $C$ , $O$ is the origin. If $| O P | = | O F |$ , then the area of $\triangle O P F$ is
A. $\frac { 3 } { 2 }$
B. $\frac { 5 } { 2 }$
C. $\frac { 7 } { 2 }$
D. $\frac { 9 } { 2 }$

Given that the ellipse $C$ has foci $F _ { 1 } ( - 1,0 ) , F _ { 2 } ( 1,0 )$, and passes through

10. Let $F$ be a focus of the hyperbola $C : \frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 5 } = 1$ . Point $P$ is on $C$ , $O$ is the origin. If $| O P | = | O F |$ , then the area of $\triangle O P F$ is\\
A. $\frac { 3 } { 2 }$\\
B. $\frac { 5 } { 2 }$\\
C. $\frac { 7 } { 2 }$\\
D. $\frac { 9 } { 2 }$

Paper Questions

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