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首页>知识点选题>抛物线上的点到定点和焦点距离的和、差最值
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已知点eqIdd5b10b2a13f148b78e0d5a1b820538fd是抛物线eqId9d0b2f7d1963449ea4d72f32d937586e的焦点,点eqIdd7be5abad1e34f6db17a56660de8d54f为抛物线上的任意一点,eqId78da143eb3cf4a69b3c2895ac3dcc407为平面上点,则eqIddb9cab54f5834162a2f895090a9d34d1的最小值为(    )
A.3B.2C.4D.eqId7bcd573cee334383ad72cc4b179fcfb3
更新:2020/04/04 难度:0.85 题型:单选题 组卷:1127
已知抛物线eqIdc821520aafa3438496715a2d6c19cacf上的点eqIdd7be5abad1e34f6db17a56660de8d54f到焦点eqIdd5b10b2a13f148b78e0d5a1b820538fd的距离为8,则eqIda6dd6e0846d747fab9e1fc7d28f7bca9eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点)的面积为( )
A.16B.8C.4D.2
更新:2020/04/02 难度:0.65 题型:单选题 组卷:302
已知抛物线eqId294af0137a7a4b2f873817ba8fbafb44的准线过点eqIdbe1458080a8c442fbbc83863be99bb06,若过焦点F的直线eqId417e80f1349244878d01fe90e0891f5f与抛物线交于AB两点,若AB两点的横坐标之和为eqId74cb882ded0b46938a9f0e630101a97c.
(1)求eqId4819509fefec4542acccfcf3d67cd699
(2)若P是抛物线上的一个动点,设eqIdd19676f8de0241efb2c8da9655ecc559,求eqId1d6b3ea325c14deaa281f496ff6c7198的最小值.
更新:2020/04/01 难度:0.65 题型:解答题 组卷:0
已知抛物线eqIdf91aad2290ad408799ceac6f8a03ae91的焦点为F(4,0),过F作直线l交抛物线于MN两点,则p=_______,eqId88d26f32bdf74422af8564270c38b687的最小值为______.
更新:2020/03/30 难度:0.65 题型:填空题 组卷:173
在抛物线eqId7eed3e099a414ab9b690fdb0e90234da上有一点eqIdbedf755e0fdb4d078d6859360706b163,它到eqId8e2dc7a51b6a48108ea0c490dd5a6b3f的距离与它到抛物线焦点距离之和最小,则eqIdbedf755e0fdb4d078d6859360706b163点坐标是(   )
A.eqId6dc34b07622a4cf687b0d2aec6869d3bB.eqId831425e0931e48bf95a5dda50d29f0f0C.eqId4f00f6196b604aa286f0c2614d8eefb1D.eqId43752ccb07464dfdadfdf89c02986f33
更新:2020/03/30 难度:0.85 题型:单选题 组卷:0
已知抛物线eqIdf91aad2290ad408799ceac6f8a03ae91与斜率为eqId37705e1ef6a84bbdbe88433e75932cdf且过抛物线焦点eqId63db14a5b4334f3ea583c8fb12b0d175的直线eqId417e80f1349244878d01fe90e0891f5f交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,满足弦长eqId641d708c12164ec48d8bde70faf46731.
(1)求抛物线的标准方程;
(2)已知eqId2381423d4cd146cab95f55527681a766为抛物线上任意一点,eqId05a3f9e9557247efa1715adb34924696为抛物线内一点,求eqIdb43c78f75f6c45d29cc024d011c727b4的最小值,以及此时点eqId2381423d4cd146cab95f55527681a766的坐标.
更新:2020/03/29 难度:0.65 题型:解答题 组卷:0
已知抛物线eqId5bd1717b032b4d77a2031af254bbf5d2的焦点eqId63db14a5b4334f3ea583c8fb12b0d175到其准线的距离为4,圆eqIddeaa2279ebaa46dc8e3fb59e1bfb11d1,过eqId63db14a5b4334f3ea583c8fb12b0d175的直线eqId417e80f1349244878d01fe90e0891f5f与抛物线eqId19a4eb16029e4550a14f2afe4741a3c3和圆eqId2381423d4cd146cab95f55527681a766从上到下依次交于eqIdcc614bd3390c4d028df189b234dcc351eqIdd7be5abad1e34f6db17a56660de8d54feqId75a143b898e14ccdb032561fba9da811eqId8754ce8cf7f34f04abb9a0c041f57f5c四点,则eqIdb707921544f143f9b08da5e25cd09653的最小值为(   )
A.9B.11C.13D.15
更新:2020/03/28 难度:0.65 题型:单选题 组卷:345