已知點(diǎn)

,動(dòng)點(diǎn)

、

分別在

、

軸上運(yùn)動(dòng),滿(mǎn)足

,

為動(dòng)點(diǎn),并且滿(mǎn)足

.
(Ⅰ)求點(diǎn)

的軌跡

的方程;
(Ⅱ)過(guò)點(diǎn)

的直線(xiàn)

(不與

軸垂直)與曲線(xiàn)

交于

兩點(diǎn),設(shè)點(diǎn)

,

與

的夾角為

,求證:

.
解:(Ⅰ)設(shè)


①
又

②
由①②可得,

(也可用作直線(xiàn)

,運(yùn)用拋物線(xiàn)的定義得出)
(Ⅱ)



設(shè)


練習(xí)冊(cè)系列答案
相關(guān)習(xí)題
科目:高中數(shù)學(xué)
來(lái)源:不詳
題型:解答題
(本小題滿(mǎn)分12分)已知向量

且

,(Ⅰ)若

與

是兩個(gè)共線(xiàn)向量,求

的值;
(Ⅱ)若

,求函數(shù)

的最小值及相應(yīng)的

的值。
查看答案和解析>>
科目:高中數(shù)學(xué)
來(lái)源:不詳
題型:解答題
(12分)設(shè)

=(4,-3),

=(2,1),是否存在實(shí)數(shù)t,使得

+t

與

的夾角為45º.若存在,求出t的值,若不存在說(shuō)明理由.
查看答案和解析>>
科目:高中數(shù)學(xué)
來(lái)源:不詳
題型:解答題
(本小題滿(mǎn)分12分)已知向量

,向量

與向量

夾角為

,且

.(1)求向量

;(2)若向量

與向量

的夾角為

,其中

,
B,

為

的內(nèi)角,且

,

,

依次成等差數(shù)列,試求|

|的取值范圍。
查看答案和解析>>
科目:高中數(shù)學(xué)
來(lái)源:不詳
題型:解答題
(本題滿(mǎn)分10分)在

中,角

、

、

所對(duì)的邊分別為

,已知向量


,且

.(1)求角

的大��; (2)若

,求

的最小值.
查看答案和解析>>
科目:高中數(shù)學(xué)
來(lái)源:不詳
題型:單選題
若向量
=(,-),
||=2,若
•(-)=2,則向量
與
的夾角為( �。�
查看答案和解析>>
科目:高中數(shù)學(xué)
來(lái)源:不詳
題型:單選題
已知向量

=(3,4),

=(sin

,cos

),且

,則tan

等于 ( )
查看答案和解析>>
科目:高中數(shù)學(xué)
來(lái)源:不詳
題型:填空題
已知三點(diǎn)

,若

為線(xiàn)段

的三等分點(diǎn),則

=.
查看答案和解析>>
科目:高中數(shù)學(xué)
來(lái)源:不詳
題型:填空題
已知

與

,要使

最小,則實(shí)數(shù)

的值為_(kāi)__________。
查看答案和解析>>