题干

已知椭圆
x
2
2
+y2=1的左右焦点分别为F1,F2,直线l过椭圆的右焦点F2与椭圆交于A,B 两点,

(Ⅰ)当直线l的斜率为1,点P为椭圆上的动点,满足使得△ABP的面积为

2
5
2
3
的点P有几个?并说明理由.

(Ⅱ)△ABF1的内切圆的面积是否存在最大值?若存在,求出这个最大值及此时直线l的方程,若不存在,请说明理由.

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答案(点此获取答案解析)

解:(Ⅰ)由题意可知:椭圆
x
2
2
+y2=1焦点在x轴上,右焦点F2(1,0),
设直线l的方程为:y=x﹣1,则

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    Both of my parents worked full-time when I was a little girl, so my grandmother would stay at our house during the day. We would watch game shows in the living room. Our favorite was The Price is Right. We would call out our answers along with the contestants.

    When I got older and started going to school, we couldn't watch our game shows regularly. That was okay with me, though, because the one thing I liked better than watching game shows with my grandmother was helping her bake. Watching her in the kitchen was amazing: she never seemed to need the recipes but everything she made tasted delicious.

    At first I would just sit in the kitchen and watch, even though I didn't understand what she was doing. As I got older, she let me help with the easy parts, such as measuring the sugar. The day she let me separate the eggs,I felt like I had found complete pleasure.

    At last, my parents decided that I could take care of myself,and my grandmother stopped coming over every day. The love of baking, however, stayed with me. I started baking by myself, and even if the cookies ended up burnt sometimes, more often they turned out pretty well. I tried out new recipes, and whenever I got to a thorny part, I would call my grandmother for advice. Sometimes I would call her just to talk, too. I felt like I could talk to her about anything.

    My grandmother passed away ten years ago, but I still think of her every day. Last week, I found a recipe book she made for me. It included her recipes for brownies, cookies, and my favorite, lemon pie. As I looked through the pages, I thought I could hear her voice. She was the one who taught me not just about baking, but about life.

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