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在平面直角坐标系中,已知eqId1b4bd063fce94d60b27b5c4e97c09e6beqIdcd41fd5b7a704b179bf50c0dc7130d8b,动点eqId9eadb467bb044d669030fbe083ff2b2f满足eqId4fdcb536f17c442ca630b3f65effa482,设动点eqId2381423d4cd146cab95f55527681a766的轨迹为曲线eqId19a4eb16029e4550a14f2afe4741a3c3
(1)求动点eqId2381423d4cd146cab95f55527681a766的轨迹方程,并说明曲线eqId19a4eb16029e4550a14f2afe4741a3c3是什么图形;
(2)过点eqIda8cefae4538f4c9b904b4491ca9f377d的直线eqId417e80f1349244878d01fe90e0891f5f与曲线eqId19a4eb16029e4550a14f2afe4741a3c3交于eqIdc3bc315778fd47ef9822f0554c98bd79两点,若eqId02fbe871afcf4aeeac27003f2635424d,求直线eqId417e80f1349244878d01fe90e0891f5f的方程;
(3)设eqIdd7be5abad1e34f6db17a56660de8d54f是直线eqId15e0fd7615304466972e88dcb40f43ea上的点,过eqIdd7be5abad1e34f6db17a56660de8d54f点作曲线eqId19a4eb16029e4550a14f2afe4741a3c3的切线eqIda15b3ea5b2ac4796987ebaa957a97f39,切点为eqIda92ef8a17f814f0d898ebab639d7d68d,设eqIdc10f5a45a6d64ab0a2d2be67365e352f,求证:过eqId23828ed16a7b462eb3502558ae39866f三点的圆必过定点,并求出所有定点的坐标.
更新:2019/8/21难度系数:0.4题型:解答题组卷:20次
求满足下列条件的圆的方程:
(1)经过点P(5,1),圆心为点C(8,-3);
(2)经过三点A(0,0),B(1,1),C(4,2).
更新:2019/8/14难度系数:0.65题型:解答题组卷:83次
在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,已知圆C经过点eqId195959dd033548d6b7d9bea37e66f86b,且圆心在直线eqIdd75f8ef820544c0fb50c323ec7d5e17f.
(1)求圆C的方程; 
(2)设P是圆eqIdc9819ded9e96439586ef7ee82303b770上任意一点,过点P作圆C的两条切线eqId69bb44c4402043568430bacafdc11741,eqId71891062a8724584af9a2c4c77cd566e为切点,试求四边形eqIdbaa557de66b64e02975121659413d35c面积eqId1b7d8b87b50e4cfdbf89d48980209a52的最小值.
更新:2019/8/13难度系数:0.4题型:解答题组卷:83次
在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,直线eqIdf7d441ad989c404e9340dd2cb9708082截以坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b为圆心的圆所得的弦长为eqId807b61b62f09462994e31cf497210538.
(1)求圆eqId2efda802d5534f6d92d9f8af7aaec28b的方程;
(2)若直线eqId417e80f1349244878d01fe90e0891f5f与圆eqId2efda802d5534f6d92d9f8af7aaec28b切于第一象限,且与坐标轴交于点eqId0cd8063abf2b458f80091bc51b75a904eqId93cbffaa5ae045d6ac45d1e979991c3a,当eqId421efa80cf9a4cbbb570968195aa1c5f时,求直线eqId417e80f1349244878d01fe90e0891f5f的方程;
(3)设eqId2381423d4cd146cab95f55527681a766eqIdd7be5abad1e34f6db17a56660de8d54f是圆eqId2efda802d5534f6d92d9f8af7aaec28b上任意两点,点eqId2381423d4cd146cab95f55527681a766关于eqIdc12aac8c2448479687a40735b3572a23轴的对称点为eqId517584fed25c413ba8b7bb33ffa2d5c6,若直线eqId931ba899d97a4e2cb3e45188a59009c9eqId1457f64a7c5a4d78ae04ddb4d86e8651分别交eqIdc12aac8c2448479687a40735b3572a23轴于点eqIdbfa767a5fea444afaf709f2b335d903eeqIdd4a0eefe83294b31965c34abd6e930db,问eqId7ee9cba96d234881be35f27c0dd43136是否为定值?若是,请求出该定值;若不是,请说明理由.
更新:2019/8/9难度系数:0.65题型:解答题组卷:96次
在平面立角坐标系eqId2272a344734c4fb088737b84294f7219中,过点eqId1036c3949e994e4f91bca65cb4abcbb2的圆的圆心eqId19a4eb16029e4550a14f2afe4741a3c3eqIdc12aac8c2448479687a40735b3572a23轴上,且与过原点倾斜角为eqId4023ceb292e24a45871ca56fa44d50e3的直线eqId417e80f1349244878d01fe90e0891f5f相切.
(1)求圆eqId19a4eb16029e4550a14f2afe4741a3c3的标准方程;
(2)点eqIdd7be5abad1e34f6db17a56660de8d54f在直线eqId19ecaec5ebff4fb99800d72213a35e23上,过点eqIdd7be5abad1e34f6db17a56660de8d54f作圆eqId19a4eb16029e4550a14f2afe4741a3c3的切线eqIddc272480cccc4b2d8c1bc77debf9c0a8eqId0ee1c782cf8f45239afc0b714644b017,切点分别为eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6,求经过eqIdd7be5abad1e34f6db17a56660de8d54feqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6eqId19a4eb16029e4550a14f2afe4741a3c3四点的圆所过的定点的坐标.
更新:2019/8/16难度系数:0.4题型:解答题组卷:53次
已知点eqIda381767fb5724ba480725d15bacd273f
(1)求eqId992fe44057cf4492895193f3f5398449eqId0627be51821d4be7b3e024a354815d64边上的高所在直线的方程;
(2)求过eqId10bbe48f886a4fa78fdf8c1fd064f9b4三点的圆的方程.
更新:2019/7/25难度系数:0.85题型:解答题组卷:392次
古希腊数学家阿波罗尼斯在他的巨著《圆锥曲线论》中有一个著名的几何问题:在平面上给定两点eqIdaea518ed575841d7970eb40681952f7deqId5eabb5785dbd419ca3235ed35bdfe4ab,动点eqIdd7be5abad1e34f6db17a56660de8d54f满足eqIde887f9e4f650401e99f68072dd7cb2cb(其中eqId70a27b6ddf6b478285353abb3b1f3741eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c是正常数,且eqIda595c361887f468086aaeccc2fb0908b),则eqIdd7be5abad1e34f6db17a56660de8d54f的轨迹是一个圆,这个圆称之为“阿波罗尼斯圆”,该圆的半径为__________.
更新:2019/7/25难度系数:0.65题型:填空题组卷:124次
已知圆eqId8e4924b5d205439a97e434443181adc6关于直线eqId8a4ed26fe47842409d88b38cfd3f699d对称,半径为eqIdc052ddfbd4524f67a79e0e77c2e5656a,且圆心eqId19a4eb16029e4550a14f2afe4741a3c3在第一象限.
(Ⅰ)求圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(Ⅱ)若直线eqId5f8741dd4b154c50862757fecf7860c4与圆eqId19a4eb16029e4550a14f2afe4741a3c3相交于不同两点eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6,且eqId570c451681d540bc8f8848bbd5edf376,求实数eqId3a4208e0040c42ed8b09de2cae9d562e的值.
更新:2019/7/25难度系数:0.65题型:解答题组卷:267次
已知二次函数eqIdef72f8bc1cc942659a17e57c1768f1a7eqIdc12aac8c2448479687a40735b3572a23轴于eqIdeb53cb7cb0274f7d8f111c60f824c243两点(eqIdeb53cb7cb0274f7d8f111c60f824c243不重合),交eqId072d7d6b911b42bc89207e72515ebf5f轴于eqId19a4eb16029e4550a14f2afe4741a3c3点. 圆eqId2381423d4cd146cab95f55527681a766eqId10bbe48f886a4fa78fdf8c1fd064f9b4三点.下列说法正确的是( )
① 圆心eqId2381423d4cd146cab95f55527681a766在直线eqId5db4a4f976ba42089c0439595abeb40b上;
② eqId3a4208e0040c42ed8b09de2cae9d562e的取值范围是eqId92e73e2b41904318ab5e3d5894a91e80
③ 圆eqId2381423d4cd146cab95f55527681a766半径的最小值为eqIdf1bd69290a464f71ac73b93c51985105
④ 存在定点eqId517584fed25c413ba8b7bb33ffa2d5c6,使得圆eqId2381423d4cd146cab95f55527681a766恒过点eqId517584fed25c413ba8b7bb33ffa2d5c6.
A.①②③B.①③④C.②③D.①④
更新:2019/7/18难度系数:0.15题型:单选题组卷:114次
若方程eqId26eac829859c42ddb873cd91b6ddb002表示一个圆,则eqId3a4208e0040c42ed8b09de2cae9d562e的取值范围是(    )
A.eqId6eee222f0e954d24ada180d3b2aa3192B.eqIdcf6b6fd1d0d04e1f85c78a2c208d884bC.eqIdcc220d5b3bd24502a2a709c426c7feb2D.eqIdc1f33feff60c48d08858c423c6803432
更新:2019/7/16难度系数:0.85题型:单选题组卷:447次
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