抛物线与直线关系如图,o为坐标原点,直线l在x轴和y轴上的截距分别是a和b（a＞0,b不等于0）,且交抛物线y2=2px
2个回答

l方程：x/a+y/b=1

x=a-ay/b

代人y^2=2px得：

y^2=2pa-2pay/b

y^2+2pay/b-2pa=0

y1+y2=-2pa/b,y1y2=-2pa

所以,

1/y1+1/y2=(y1+y2)/y1y2

=(-2pa/b)/(-2pa)

=1/b

tan∠MON=(Kmo+Kno)/(1-Kmo*Kno)

=(y1/x1+y2/x2)/(1-y1y2/x1x2)

=(2p/y1+2p/y2)/(1-y1y2/x1x2)

=2p(1/y1+1/y2)/(1-y1y2/x1x2)

=2p/b(1-y1y2/x1x2)

=2p/b(1-y1y2/(y1^2*y2^2/4p^2))

=2p/b(1-4p^2/y1y2)

=2p/b(1-4p^2/(-2pa))

=2p/b(1+2p/a)

=2p/b(1+2p/2p)

=2p/2b

=p/

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