Question

一道高三数学题求大神解答！！要详细解答过程谢谢！！

Answer 1

F(1,0).
(1)设M(1，m),A(1-h,m-k),B(1+h,m+k),
A,B在抛物线y^2=4x上，
∴|FA|+|FB|=2-h+2+h=4.
(2)设M(t，m),A(t-h,m-k),B(t+h,m+k),
A,B在抛物线y^2=4x上，
∴(m-k)^2=4(t-h),①
(m+k)^2=4(t+h),②
②-①，4km=8h,m=2h/k,
(①+②)/2,m^2+k^2=4t,
4h^2/k^2+k^2=4t,
4h^2=k^2(4t-k^2)
AB^2=4h^2+4k^2
=k^2(4t-k^2)+4k^2
=-k^4+(4t+4)k^2
=-[k^2-(2t+2)]^2+(2t+2)^2,t>0,
∴|AB|的最大值g(t)=2t+2.