已知AB是抛物线Y方=4X的焦点弦,其坐标A(X1,X2)B(X2,Y2)满足X1+X2=6,则AB=
问题描述:
已知AB是抛物线Y方=4X的焦点弦,其坐标A(X1,X2)B(X2,Y2)满足X1+X2=6,则AB=
如题、
答
焦点为:(1,0)设AB方程为:y=k(x-1)y1+y2=k(x1+x2)-2k=6k-2k=4ky1^2=4x1,y2^2=4x2y1^2-y2^2=4(x1-x2)(y1-y2)/(x1-x2)=4/(y1+y2)=4/4k=1/k所以,k=1/kk^2=1把y=±(x-1)代入Y方=4X得:(x-1)^2=4xx^2-6x+1=0x1+x2=6,x1x...