only me and the moon歌詞

《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.