解析几何,第一题答案y平方=4x,求2答:(1)y^2=4x.(2)对上式求导得2yy'=4,y'=2/y,设M(m^2,2m),N(n^2,2n),m≠n,则 切线MQ:y-2m=(x-m^2)/m,即x-my+m^2=0,NQ:x-ny+n^2=0,它们都过Q(q,2q+2),∴q-m(2q+2)+m^2=0,q-n(2q+2)+n^2=0,∴m,n是方程x^2-(2q+2)x+q=0的两根,m+n=2...
过y的平方=4x的焦点F作两条互相垂直的弦AB和DE,求向量AD乘向量EB最...答:抛物线y^2=4x①的焦点是F(1,0),设弦AB:x=my+1,② 代入①,y^2-4my-4=0,设A(x1,y1),B(x2,y2),则 y1+y2=4m,y1y2=-4.由②,x1+x2=m(y1+y2)+2=4m^2+2,x1x2=(my1+1)(my2+1)=m^2y1y2+m(y1+y2)+1=1,弦DE⊥AB,设D(x3,y3),E(x4,y4),则 y3+y4=...