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  • 當前位置:首頁 > 活動方案 > 教學設計 > 《橢圓的參數方程》導學案

    《橢圓的參數方程》導學案

    時間:2019-06-19 11:06來源:http://www.16mnyg.com點擊:

    《橢圓的參數方程》導學案

    【學習目標】
    (1)理解橢圓參數方程的形成過程和參數的幾何意義;
    (2)會進行橢圓參數方程與普通方程之間的互化;
    (3)會用橢圓的參數方程解決動點最值的相關問題。
    【重點難點】
    重點:橢圓參數方程的形成過程;橢圓參數方程解決動點最值問題;
    難點:參數的幾何意義。
    【學法指導】
    引導探究法,啟發式教學
    【學習過程】
    問題1:圓心在原點,半徑為 的圓的參數方程是什么?


    參數的幾何意義:
    問題2:
    如下圖,以原點為圓心,分別以 為半徑作兩個圓,點 是大圓半徑 與小圓的交點,過點 作 ,垂足為 ,過點 作 ,垂足為 。當半徑 繞點 旋轉時,點 的軌跡是什么?

    問題3:圓的參數方程中,引入了旋轉角 作為參數,橢圓中可以引入哪個變量作為參數?

    問題4:為什么引入 作為參數?

    問題5:怎樣建立橢圓的參數方程?

    問題6:怎樣說明這個參數方程表示的就是橢圓?


    問題7:參數 有怎樣的幾何意義?

    橢圓的參數方程中 的幾何意義與圓的參數方程中 的幾何意義相同嗎?
    總結:橢圓 的參數方程為:


    課堂練習:
    (1) 橢圓 的參數方程為:

    (2)  ( 為參數)普通方程為:

    例1. 求橢圓 的內接矩形的最大面積。

    例2.  在平面直角坐標系 中,點 是橢圓 上的動點;(1)求 的最大值;

    (2)求點 到直線 距離的最小值。


    小結:這節課你學到了什么?

    課后思考:(1)推導焦點在 軸上橢圓的參數方程;
              (2)橢圓還有別的參數方程形式嗎? 本文來源心得體會范文網。轉載請注明出處:http://www.16mnyg.com/fangan/sheji/35813.html(責任編輯:topbys.com)

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