我们把焦点相同，且离心率互为倒数的椭圆和双曲线称为一对“相关曲线”．已知F1、F2是一对相关曲线的焦点，P是它们在第一象限的交点，当∠F1PF2=60°时，这一对相关曲线中双曲线的离心率是（ ）
|
设F1P=m，F2P=n，F1F2=2c，
由余弦定理得（2c）2=m2+n2-2mncos60°，
即4c2=m2+n2-mn，
设a1是椭圆的实半轴，a2是双曲线的实半轴，
由椭圆及双曲线定义，得m+n=2a1，m-n=2a2，
∴m=a1+a2，n=a1-a2，
将它们及离心率互为倒数关系代入前式得a12-4a1a2+a12=0，
a1=3a2，e1•e2=
•c a1
=c a2
=1，(
)2c a2 3
解得e2=
．3
故选A．
| 完形填空。 | ||||
| I arrived in London on a foggy day to go to a very important meeting. The place where the meeting was going to be 1 was on the other side of the town. All traffic came to 2 because the drivers were not able to see more than a yard in front of them. The meeting would begin at nine o'clock, so I decided to go there 3 . Minutes later, I was completely 4 . I stood there, saying unpleasant things about the fog, and thinking that I 5 to phone to the meeting to explain that was not able to arrive there on time. Then I heard a young man's voice coming out of the fog, "I suppose you are lost. Can help you?" I was very glad to have a man who 6 take me to the meeting. Afterward I 7 him where I wanted to go, took him by the arm, and we started. We walked quite fast, turning 8 and crossing roads in some places. 9 I followed him through the dark street, I wondered why he found his way easily. "I know this part of London quite well," he said, "But in such a fog it's impossible to see anything," I said. "I am 10 , sir." He answered. "In the fog it is exactly the same for me as usual." | ||||
|