在直角坐标系中,已知抛物线y2在直角坐标系中,已知抛物线y2=2px,过点(2p,0)作直线,交抛物线于ab两点给出下列结论(1)oa⊥ob,(2)S△OABmin=4p2(3)x1x2=-4p2.其中正确的结论是

Question

在直角坐标系中,已知抛物线y2在直角坐标系中,已知抛物线y2=2px,过点(2p,0)作直线,交抛物线于ab两点给出下列结论(1)oa⊥ob,(2)S△OABmin=4p2(3)x1x2=-4p2 .其中正确的结论是

Answer 1

L:y=k(x-2p)
y^2=2px
k^2*(x-2p)^2=2px
k^2*x^2-(2p+4pk^2)x+4p^2*k^2=
x1*x2=4p^2
y1*y2=-4p^2
x1*x2+y1*y2=0
(y1/x1)*(y2/x2)=-1
x=2p,y=|2p|
s(min)=4p^2
(1),(2)正确