gaokao 2020 Q11

gaokao · China · national-III-science 5 marks Conic sections Eccentricity or Asymptote Computation

For the hyperbola $C : \frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > 0 , b > 0 )$ with left and right foci $F _ { 1 } , F _ { 2 }$ respectively, the eccentricity is $\sqrt { 5 }$ . $P$ is a point on $C$ such that $F _ { 1 } P \perp F _ { 2 } P$ . If the area of $\triangle P F _ { 1 } F _ { 2 }$ is 4 , then $a =$
A. $1$
B. $2$
C. $4$
D. $8$

For the hyperbola $C : \frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > 0 , b > 0 )$ with left and right foci $F _ { 1 } , F _ { 2 }$ respectively, the eccentricity is $\sqrt { 5 }$ . $P$ is a point on $C$ such that $F _ { 1 } P \perp F _ { 2 } P$ . If the area of $\triangle P F _ { 1 } F _ { 2 }$ is 4 , then $a =$

A. $1$

B. $2$

C. $4$

D. $8$

Paper Questions

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