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首页>高中数学综合库>平面解析几何>圆锥曲线>曲线与方程>用曲线方程研究曲线性质>由方程研究曲线的性质
题型:填空题 难度:0.4 引用次数:537 更新时间:2020/3/26 11:11:50 题号:6726658
已知曲线eqId19a4eb16029e4550a14f2afe4741a3c3的方程eqIde707707efcce411e9e95c801987ca0c8,给出下列eqIdddd35c5d043e4ebeac32a99367053c68个结论:
①曲线eqId19a4eb16029e4550a14f2afe4741a3c3是以点eqId4c1d443af674451aa43ffa4f754e6b03eqId54d26c3b27524287934469736797c36b为焦点的椭圆的一部分;
②曲线eqId19a4eb16029e4550a14f2afe4741a3c3关于eqId8e15963708e9415da25069fea5906e24轴、eqId072d7d6b911b42bc89207e72515ebf5f轴、坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b对称;
③若点eqIda733cd9df1394d929d03733bfeda55f8在曲线eqId19a4eb16029e4550a14f2afe4741a3c3上,则eqId54c6f8f452644bbcab90cc703e838208eqId9e9fa19272c84cdcb5a7baa124edb7c7
④曲线eqId19a4eb16029e4550a14f2afe4741a3c3围成的图形的面积是eqId26f1d01cdbbc4f73909a617af5e3e6a2
其中,所有正确结论的序号是__________

类题推荐

【推荐1】eqIdd894e9f5cc2e42e5b2d8d70eaadccc3b,则eqId0cd8063abf2b458f80091bc51b75a904的最小值为______.
更新:2020/01/05难度:0.4题型:填空题组卷:104
【推荐2】数学中有许多形状优美、寓意美好的曲线,曲线eqId0710a865d40e4eb8ba04d73d8cb1a340就是其中之一(如图),给出下列三个结论:
figure
①曲线eqId19a4eb16029e4550a14f2afe4741a3c3恰好经过4个整点(即横、纵坐标均为整数的点);
②曲线eqId19a4eb16029e4550a14f2afe4741a3c3上任意一点到原点的距离都不超过eqId65021072e3ee4edc934739d219c8c5e2.
③曲线eqId19a4eb16029e4550a14f2afe4741a3c3所围成的“花形”区域的面积小于4.
其中,所有正确结论的序号是_______.
更新:2020/03/15难度:0.4题型:填空题组卷:111
【推荐3】已知eqId58cb076539a74a23a795a4c04dc5fb2eeqIdd36037dacfa34f4ba9929d4ac28235deeqIdc03a5edfae9a431ea662643fb82ed401eqId920803d8ac23440095bc5147cc38c180eqId74bbc24870024225839a04b724ab6d91eqId6ff1592dae254ecea4582c09956e03d8eqId21dc87f88abc4e938d213b6ca89aaf15.给出以下四个命题:
①分别过点eqId2e6817a3ca354207937b9c8ddf163bdeeqId4994782954ec4c96831dd8999e8d85c1,作eqId920803d8ac23440095bc5147cc38c180的不同于eqId8e15963708e9415da25069fea5906e24轴的切线,两切线相交于点eqId2381423d4cd146cab95f55527681a766,则点eqId2381423d4cd146cab95f55527681a766的轨迹为椭圆的一部分;
②若eqId920803d8ac23440095bc5147cc38c180eqId6ff1592dae254ecea4582c09956e03d8相切于点eqId7412be7a456647e695421020b620936e,则点eqId7412be7a456647e695421020b620936e的轨迹恒在定圆上;
③若eqId920803d8ac23440095bc5147cc38c180eqId6ff1592dae254ecea4582c09956e03d8相离,且eqId8f453040887740999a7ea9ddf81d0a3e,则与eqId920803d8ac23440095bc5147cc38c180eqId6ff1592dae254ecea4582c09956e03d8都外切的圆的圆心在定椭圆上;
④若eqId920803d8ac23440095bc5147cc38c180eqId6ff1592dae254ecea4582c09956e03d8相交,且eqIdb527c32cb36544f6af87485d3c185f62,则与eqId920803d8ac23440095bc5147cc38c180eqId6ff1592dae254ecea4582c09956e03d8一个内切一个外切的圆的圆心的轨迹为椭圆的一部分.
则以上命题正确的是__________.
更新:2020/07/10难度:0.4题型:填空题组卷:15