问题 填空题

在△ABC中,∠A=15°,∠B=105°,若以A,B为焦点的椭圆经过点C.则该椭圆的离心率e=______.

答案

∵△ABC中,∠A=15°,∠B=105°,

设三角形外接圆半径为R,则有正弦定理得:

∴|AB|=2RsinC=2Rsin60°,|BC|=2RsinA=2Rsin15°,|AC|=2RsinB=2Rsin105°.

∵椭圆以B,C为焦点,且经过A点,

∴2a=|AC|+|CB|,2c=|BA|

∴椭圆离心率e=

c
a
=
2c
2a
=
|BA|
|AC|+|BC|
=
2Rsin60°
2Rsin15°+2Rsin105°
=
sin60°
sin15°+sin105°
=
sin60°
sin(60°-45°)+sin(60°+45°)
=
sin60°
(sin60°cos45°-cos60°sin45°)+(sin60°cos45°+cos60°sin45°)
=
sin60°
2sin60°cos45°
=
1
2
=
2
2

故答案为:

2
2

单项选择题

Generally speaking, a British is widely regarded as a quiet, shy and conservative person who is (1) only among those with whom he is acquainted. When a stranger is at present, he often seems nervous, even (2) . You have to take a commuter train any morning or evening to (3) the truth of this.

Serious-looking businessmen and women sit reading their newspapers or dozing in a corner; hardly anybody talks, since to do so would be considered quite (4) .

(5) , there is an unwritten but clearly understood code of behavior which, once broken, makes the offender immediately the object of (6) .

It has been known as a fact that a British has a (7) for the discussion of their weather and that, if given a chance, he will talk about it (8) .

Some people argue that it is because the British weather seldom (9) forecast and hence becomes a source of interest and (10) to everyone.

This may be so. (11) a British cannot have much (12) in the weathermen, who, after promising fine, sunny weather for the following day, are often proved wrong (13) a cloud over the Atlantic brings rainy weather to all districts! The man in the street seems to be as accurate — or as inaccurate — as the weathermen in his (14) .

Foreigners may be surprised at the number of references (15) weather that the British (16) to each other in the course of a single day. Very often conversational greetings are (17) by comments on the weather. “Nice day, isn’t it” “Beautiful!” may well be heard instead of “Good morning, how are you” Although the foreigner may consider this exaggerated and comic, it is (18) .pointing out that it could be used to his advantage. If he wants to start a conversation with a British but is at a loss to know (19) to begin, he could do well to mention the state of the weather. It is a safe subject which will (20) an answer from even the most reserved of the British.

6()

A.compassion

B.opposition

C.criticism

D.assault

单项选择题