组卷网>知识点选题>定义转化法求距离的最值问题
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解答题 | 一般(0.65) | 2021·全国高三专题练习
1 . 设线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3两端点在抛物线eqIdae3ada09161c4630865ac5d212317b1f上移动,M为线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3的中点,eqIdfece9b4b7fc045b79cdde07901d7a95e(a为大于零的常数),求My轴的最短距离.
解答题 | 一般(0.65) | 2021·全国高二课时练习
2 . 已知定长为eqId8f65c930571d4ff6aa6a50029d46826e的线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3的两端点在抛物线eqIdd050af449075401299cc78c647d310e8上移动,试求线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3的中点eqId2381423d4cd146cab95f55527681a766eqId072d7d6b911b42bc89207e72515ebf5f轴的最短距离.
填空题 | 较易(0.85) | 2021·全国高二课时练习
3 . 已知点eqId2381423d4cd146cab95f55527681a766为抛物线eqId7e148e9b5def4bf1af4353dbf1ccc544上一点,若点eqId2381423d4cd146cab95f55527681a766到两定点eqId18b83c6c0ea0450a9b2916ce4dacdc78eqId2c1c1a669a2f4796a571541a48af02e7的距离之和最小,则点eqId2381423d4cd146cab95f55527681a766的坐标为______
5 . 已知eqIdbedf755e0fdb4d078d6859360706b163是抛物线eqIdd050af449075401299cc78c647d310e8上的一动点,eqId63db14a5b4334f3ea583c8fb12b0d175是抛物线的焦点,点eqId06e1015a203e4bffb02af7e34df8520c,则eqId4bc69833eac94be8a322f410f2fcdbc5的最小值为(   )
A.eqId8898c1dc81824f3098bbeae74e8f11fdB.eqId7bcd573cee334383ad72cc4b179fcfb3C.eqIdddd35c5d043e4ebeac32a99367053c68D.eqId03859367a9b64a56ab90e31a0cec909a
单选题 | 一般(0.65) | 2021·全国高二课时练习
6 . 已知直线eqId377a1a863b7c4d568cabbf530025b234和直线eqId9d53e46120f34fb98eba910a8a493dbb,则抛物线eqIdd050af449075401299cc78c647d310e8上一动点eqIdbedf755e0fdb4d078d6859360706b163到直线eqId74c7e0292b094e54ae596d37798a05ed和直线eqId439fb93f7745417b8bb1747d963c6e60的距离之和的最小值是(   )
A.eqId801221b85ed147bba6ce222ebce7d57eB.2C.eqId6910b6f3fd0a4f9b81eec48da1e88ec8D.3
解答题 | 较易(0.85) | 2021·全国高二课时练习
7 . 已知点eqId87f4b27601d0409a81c95806be9d9657为抛物线eqId6a37f0e76fa244c09e4f002066995208的焦点.
说明: figure
(1)设eqId7129862151b74328b7fb0abb92b948b3,动点eqIdbedf755e0fdb4d078d6859360706b163eqId19a4eb16029e4550a14f2afe4741a3c3上运动,证明:eqIdfcff1b8cd4af431fae5d27544e377610.
(2)如图,直线eqId78f4f0478cbd4294a7dc036899b567e3eqId19a4eb16029e4550a14f2afe4741a3c3交于eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6两点(eqId2381423d4cd146cab95f55527681a766在第一象限,eqId517584fed25c413ba8b7bb33ffa2d5c6在第二象限),分别过eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6eqId417e80f1349244878d01fe90e0891f5f的垂线,交eqId072d7d6b911b42bc89207e72515ebf5f轴于eqId312ef2c826304089b9b0f1d1e88b0f50eqId93cbffaa5ae045d6ac45d1e979991c3a两点,求eqId89dca4eaaea54ad18da8aa21b6737a36的取值范围.
多选题 | 一般(0.65) | 2021·全国高二课时练习
8 . 已知抛物线eqId274969f8d14c44418fcdf003c437a3a3的焦点为eqId63db14a5b4334f3ea583c8fb12b0d175,圆eqId3fcd8a66f64b44f8aa8aaf5b448b35ea与抛物线eqId93cbffaa5ae045d6ac45d1e979991c3a交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,点eqIdbedf755e0fdb4d078d6859360706b163为劣弧eqId1609e6778d084a1d9bb2bf4111fcf29a上不同于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c的一个动点,过点eqIdbedf755e0fdb4d078d6859360706b163作平行于eqId072d7d6b911b42bc89207e72515ebf5f轴的直线eqId417e80f1349244878d01fe90e0891f5f交抛物线eqId93cbffaa5ae045d6ac45d1e979991c3a于点eqId517584fed25c413ba8b7bb33ffa2d5c6,则(   )
A.点eqIdbedf755e0fdb4d078d6859360706b163的纵坐标的取值范围是eqIdcbf8afa399284910896111eaabf94aa3
B.eqId0044ff82e952440d902a5fd50f66128e等于点eqIdbedf755e0fdb4d078d6859360706b163到抛物线eqId93cbffaa5ae045d6ac45d1e979991c3a的准线的距离
C.圆eqId19a4eb16029e4550a14f2afe4741a3c3的圆心到抛物线eqId93cbffaa5ae045d6ac45d1e979991c3a的准线的距离为2
D.eqId53c0ffff5e4a47dca3b2bc8acebf93eb周长的取值范围是eqId60ba39785b6f4af4933ff5b7a04e6e55
单选题 | 较易(0.85) | 2021·全国高二课时练习
9 . 已知点eqIdbedf755e0fdb4d078d6859360706b163是抛物线eqId082a75f3699e40bf92e7d248364c1918上的动点,点eqIdbedf755e0fdb4d078d6859360706b163eqIda9cd3f94eb8045438f75e9daccfa7200轴上的射影是点eqId75a143b898e14ccdb032561fba9da811,点eqId052844cae8574a8ab842c38a039baac0的坐标是eqId909dd6038fbb41e08e0af89063a50bdd,则eqId3a5f1d40140a4490b96ec74d84974c55的最小值为(   )
A.7B.8C.9D.10
10 . 定长为6的线段AB两个端点在抛物线eqIdd050af449075401299cc78c647d310e8上移动,记线段AB的中点为M,则My轴距离的最小值为(   )
A.eqId7c83ccf5b4e742538f181cb75d127445B.eqIda515a9acf7de48c193122a37ba80e98fC.2D.eqIdd5cb452414a444dc8b1ac690807a8959