gaokao 2025 Q10

gaokao · China · national-I 6 marks Conic sections Focal Chord and Parabola Segment Relations

Let the focus of parabola $C: y^2 = 6x$ be $F$. A line through $F$ intersects $C$ at $A$ and $B$. A line through $F$ perpendicular to $AB$ intersects the directrix $l: x = -\frac{3}{2}$ at $E$. From point $A$, draw a perpendicular to the directrix $l$ with foot $D$. Then
A. $|AD| = |AF|$
B. $|AE| = |AB|$
C. $|AB| \geq 6$
D. $|AE| \cdot |BE| \geq 18$

Let the focus of parabola $C: y^2 = 6x$ be $F$. A line through $F$ intersects $C$ at $A$ and $B$. A line through $F$ perpendicular to $AB$ intersects the directrix $l: x = -\frac{3}{2}$ at $E$. From point $A$, draw a perpendicular to the directrix $l$ with foot $D$. Then\\
A. $|AD| = |AF|$\\
B. $|AE| = |AB|$\\
C. $|AB| \geq 6$\\
D. $|AE| \cdot |BE| \geq 18$

Paper Questions

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