Given ellipse C : x 2 /a 2 +y 2 /b 2 =1 ( a>b>0 ). Ellipse C passes through the point P : (1,3/2) , and has eccentricity e=1/2 . Given line ℓ : x=4 . AB is the chord that intersects line ℓ on point M , and F is the right focus of ellipse C . The slopes of PA , P B , and PM are respectively k1 , k2 , and k3 . Is there a constant λ that satisfies k1+k2=λk3 ? If there is, please calculate λ .
