《Only Me and the Moon》的歌詞如下:
Oh, the world is full of love
世界充滿愛
But it's only me and the moon
但只有我和月亮
When I look up at the stars
當我仰望星空
I don't know which one is you
我不確定哪一顆是你
We were close as friends
我們是親密的朋友
Till your love went deeper than friendships can bear
直到你的愛超出了朋友的承受範圍
Oh, it was the time of our lives
那是一段我們生命中最美好的時光
And I know we'll meet again some day
我知道我們有一天會再次相遇
But till then
但直到那一天
Oh, it's only me and the moon
只有我和月亮
I miss your arms around me
我想念你擁抱著我
And your warm embrace
和你的溫暖擁抱
I miss your tender touch
我想念你的溫柔觸碰
And the way you always used to care
和你總是關心的方式
And though our paths may never cross again
雖然我們的路可能不會再交叉了
I'll always remember how you were my guiding light
我會永遠記得你是我的指引之光
Oh, the world is full of people
世界充滿了人
But they're not you
他們不是你
When I look up at the stars
當我仰望星空時
I can see you smiling back at me
我可以看到你回饋我的微笑
Oh, it's only me and the moon
只有我和月亮
Lyrics by 小蠻若寂(雙曲線x2a2-y2b2=1(a>0,b>0)的一條漸近線與圓x2+y2=a2相切,則雙曲線的離心率e的值為______.
解:雙曲線的一條漸近線方程為$bx + ay = 0$,即$y = - \frac{b}{a}x$,圓$x^{2} + y^{2} = a^{2}$的圓心為$(0,0)$,半徑為$a$,則圓心到漸近線的距離為$\frac{b^{2}}{a^{2} + b^{2}}$,即$\frac{b^{2}}{c}$,由題意可得$\frac{b^{2}}{c} = \frac{a}{c}$,即$e = \sqrt{1 + \frac{b^{2}}{a^{2}}} = \sqrt{2}$.
故答案為:$\sqrt{2}$.
根據題意,求出雙曲線的漸近線方程為$bx + ay = 0$,將圓的方程變形可得圓心為$(0,0)$,半徑為$a$,由點到直線的距離公式可得圓心到漸近線的距離為$\frac{b^{2}}{a^{2} + b^{2}}$,由題意可得$\frac{b^{2}}{a^{2} + b^{2}} = \frac{a}{c}$,變形可得$e = \sqrt{1 + \frac{b^{2}}{a^{2}}}$的值,即可得答案.
本題考查雙曲線的漸近線方程以及雙曲線的離心率,注意分析雙曲線的漸近線與圓的位置關係.