gaokao 2025 Q10

gaokao · China · national-I_eol 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 perpendicular from $A$ to the line $l: x = -\frac{3}{2}$ meets it at $D$. A line through $F$ perpendicular to $AB$ meets $l$ at $E$. 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 perpendicular from $A$ to the line $l: x = -\frac{3}{2}$ meets it at $D$. A line through $F$ perpendicular to $AB$ meets $l$ at $E$. Then\\
A. $|AD| = |AF|$\\
B. $|AE| = |AB|$\\
C. $|AB| \geq 6$\\
D. $|AE| \cdot |BE| \geq 18$

Paper Questions

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