问题 解答题
已知椭圆C经过点A(0,2),B(
1
2
3
).
(Ⅰ)求椭圆C的方程.
(Ⅱ)设P(x0,y0)为椭圆C上的动点,求x20+2y0的最大值.
答案

(1)设所求的椭圆方程为mx2+nb2=1,(m,n>0).

由于椭圆C经过点A(0,2),B(

1
2
3
),

0+4n=1
m
4
+3n=1
,解得m=1,n=
1
4

因此所求椭圆C的方程为:

y2
4
+x2=1.

(2)∵P为椭圆上的动点,∴

y20
4
+x20=1.

∴x

20
+2y0=1-
y20
4
+2y0=-
1
4
(y0-4)2+5,-2≤y0≤2

当y0=2时,

x20
+2y0取最大值4.

阅读理解

根据短文内容选择最佳答案。

One day when I was 9 years old, I was lost when I went shopping with my parents.

I walked and looked for my parents. I did not know what to do. When I wanted to cry, I remembered my father’s words that I was now "a big girl" and then I walked bravely (勇敢地).

I went to the bookstore on the first floor. My father wanted to get some books just now, but my parents were not there. Then, I went to the shoe shop on the second floor. My mother went to buy a pair of shoes. I did not find them there. "Did they go home? How could I get home then? "I was very worried (焦虑的).

Then an idea came up. I ran to the Information Counter (信息台). I told the clerk that I was lost. The news went out over the loud speakers of the shopping center.

My parents arrived at the counter later. They looked worried, too, but I was happy for finding them.

小题1:Where did the girl get lost in this article?

A. In a bookstore.       B. In a shopping center.     C. In a shoe shop.

小题2:What did the girl do when she was lost?

A. She stayed there and cried. B. She went home by herself. C. She looked for her parents.

小题3:How did the girl’s parents look when they found her?

A. They looked worried.   B. They looked surprised.   C. They looked unfriendly.

小题4:The words "loud speakers" mean _____ in Chinese.

A. 讲演者           B. 收银员            C. 扬声器

小题5:What do you know about the girl in the article?

A. She is kind but not clever.

B. She is beautiful and funny.

C. She is brave and smart.

多项选择题