gaokao 2024 Q16

gaokao · China · national-I_github 15 marks Conic sections Triangle or Quadrilateral Area and Perimeter with Foci

(15 points) Given that $A ( 0,3 )$ and $P \left( 3 , \frac { 3 } { 2 } \right)$ are two points on the ellipse $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > b > 0 )$ .
(1) Find the eccentricity of $C$ ;
(2) If a line $l$ through $P$ intersects $C$ at another point $B$ , and the area of $\triangle A B P$ is 9 , find the equation of $l$ .

(15 points)\\
Given that $A ( 0,3 )$ and $P \left( 3 , \frac { 3 } { 2 } \right)$ are two points on the ellipse $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > b > 0 )$ .\\
(1) Find the eccentricity of $C$ ;\\
(2) If a line $l$ through $P$ intersects $C$ at another point $B$ , and the area of $\triangle A B P$ is 9 , find the equation of $l$ .

Paper Questions

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