Question

已知抛物线C:y2=2px的焦点坐标F(2,0),过F的直线l交抛物线C于A,B两点,已知点M(1,0),

Answer 1

F(2,0)

p=4

y^2=8x,a>0,b>0,d>0,e>0

A(2a^2,4a),B(2b^2,-4b),D(2d^2,-4d),E(2e^2,4e)

a=b,d=e

k(AB):k(DE)=1

a≠b

k(AB)=2/(a-b),k(DE)=2/(e-d)

k(AB)=4a/(2a^2-2)=-4b/(2b^2-2)

ab=1.(1)

k(AD)=4a/(2a^2-1)=-4d/(2d^2-1)

2ad=1.(2)

k(BE)=-4b/(2b^2-1)=4e/(2e^2-1)

2be=1.(3)

(1),(2),(3):

a=2e,b=0.5/e,d=0.25/e

k(AB)=2/(a-b)=2/(2e-0.5/e)=4e/(4e^2-1)

k(DE)=2/(e-d)=2/(e-0.25/e)=8e/(4e^2-1)

k(AB):k(DE)=1/2