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  • 如图,椭圆\(C_{1}: \dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1(a > b > 0)\)的离心率为\( \dfrac { \sqrt {2}}{2}\),\(x\)轴被曲线\(C_{2}:y=x^{2}-b\)截得的线段长等于\(C_{1}\)的短轴长\(.C_{2}\)与\(y\)轴的交点为\(M\),过坐标原点\(O\)的直线\(l\)与\(C_{2}\)相交于点\(A\)、\(B\),直线\(MA\),\(MB\)分别与\(C_{1}\)相交于点\(D\)、\(E\).
    \((1)\)求\(C_{1}\)、\(C_{2}\)的方程;
    \((2)\)求证:\(MA⊥MB\).
    \((3)\)记\(\triangle MAB\),\(\triangle MDE\)的面积分别为\(S_{1}\)、\(S_{2}\),若\( \dfrac {S_{1}}{S_{2}}=λ\),求\(λ\)的取值范围.
    【考点】直线与圆锥曲线相交的弦长,椭圆的概念及标准方程,抛物线的概念及标准方程
    【分析】请登陆后查看
    【解答】请登陆后查看
    难度:较易
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