问题 选择题
过抛物线y2+8x=0的焦点且倾斜角为45°的直线l与曲线C:x2+y2-2y=0相交所得的弦的弦长为(  )
A.
2
B.2C.4D.1
答案

∵抛物线y2+8x=0的焦点F(-2,0),

∴直线l的方程为y=x+2,

把y=x+2代入曲线C:x2+y2-2y=0,并整理,得

2x2+2x=0,

解得直线l与曲线C的交点坐标为(0,2)和(-1,1),

∴所得的弦的弦长=

(0+1)2+(2-1)2
=
2

故选A.

阅读理解

根据短文内容,从短文后的选项中选出能填入空白处的最佳选项,并在答题卡上将该选项涂黑。选项中有两项为多余选项。

Many people experience feelings of sadness, and depression in winter.    小题1:   

Make a plan

The winter months can often seem quite dull, many of us spending the majority of our time indoors. A good way to get rid of this feeling is to break out of your routine and create something to look forward to.  小题2:   Whatever your plan, make sure it is something you feel excited.

Get creative about fitness

    小题3: However, many of us find our workout routine takes a hit when the cold weather sets in. To stay inspired to exercise, try searching for something new like an unusual sport.

Cheer up your social life

As people retreat more indoors to the warmth of their homes, it can feel as though your social life has gone into hibernation.(冬眠)  If you want to improve your social life, it’s time to get active. Pick up the phone and make plans to s 小题4:   spend time with friends and family.

  小题5:  

To improve your happiness over the winter, it is important to make time for those little things that improve your mood. Make a list of the day-to-day things that make you happy——such as having a catch-up with a friend, or listening to your favorite song. Planning regular treats not only gives you something to look forward to, it can also improve each day.

A.Treat yourself

B.Get an indoor hobby

C.Different people have different hobbies, so try to find one everyone can join in.

D.Exercise is a great way to beat the blues as it will leave you looking great.E. However, spending time with others can be one of the greatest mood supporters.

F. This could be a night out or weekend away, or something ongoing like a new fitness challenge.

G. If the winter blues are starting to set in, check out these ways to improve your happiness this winter.  

问答题