Question: Ellipse C: x 2 /a 2 + y 2 /b 2 =1 (a>b>0). Ellipse C pass through point P (1,3/2), Eccentricity e=1/2. Line l: x=4.

Ellipse C: x ²/a ²+ y ²/b ²=1 (a>b>0). Ellipse C pass through point P (1,3/2), Eccentricity e=1/2. Line l: x=4. AB is the chord that intersect with line l on point M, And F is the right foci of ellipse C. The slopes of PA ,PB, PM are respectively k ₁, k ₂, k ₃. Is there a constant λ that meets k ₁+ k ₂=λ k ₃? If there is a constant λ that meets k ₁+ k ₂=λ k _3, calculate λ . P. A'

P. A'

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