gaokao 2022 Q11

gaokao · China · national-I Conic sections Tangent and Normal Line Problems

11. Let $O$ be the origin. Point $A ( 1,1 )$ lies on the parabola $C : x ^ { 2 } = 2 p y$ ( $p > 0$ ). A line through point $B ( 0 , - 1 )$ intersects $C$ at points $P$ and $Q$. Then
A. The directrix of $C$ is $y = - 1$
B. Line $A B$ is tangent to $C$
C. $| O P | \cdot | O Q | > | O A | ^ { 2 }$
D. $| B P | \cdot | B Q | > | B A | ^ { 2 }$

11. Let $O$ be the origin. Point $A ( 1,1 )$ lies on the parabola $C : x ^ { 2 } = 2 p y$ ( $p > 0$ ). A line through point $B ( 0 , - 1 )$ intersects $C$ at points $P$ and $Q$. Then\\
A. The directrix of $C$ is $y = - 1$\\
B. Line $A B$ is tangent to $C$\\
C. $| O P | \cdot | O Q | > | O A | ^ { 2 }$\\
D. $| B P | \cdot | B Q | > | B A | ^ { 2 }$

Paper Questions

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