组卷网>知识点选题>定义法求焦点弦
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| 共计 231 道试题
双空题 | 一般(0.65) | 2021·湖南高二期末
解题方法
1 . 已知圆eqIdc629ed374ef34de89e12d160377610d9与抛物线eqId082a75f3699e40bf92e7d248364c1918相交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,eqId63db14a5b4334f3ea583c8fb12b0d175为抛物线的焦点,若直线eqId417e80f1349244878d01fe90e0891f5f与抛物线相交于eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6两点,且与圆相切,切点eqId0cd8063abf2b458f80091bc51b75a904在劣弧eqId1609e6778d084a1d9bb2bf4111fcf29a上,当直线eqId417e80f1349244878d01fe90e0891f5f的斜率为0时,eqId093906e4b9f04743ac7b66ba60abae11______;当直线eqId417e80f1349244878d01fe90e0891f5f的斜率不确定时,eqId778ff2d26db44941bebdbcd0de964356的取值范围是______
填空题 | 较易(0.85) | 2021·湖北高二期末
解题方法
2 . 已知抛物线eqIde73f68c98d7c4129b2a24eed090438df的焦点为eqId63db14a5b4334f3ea583c8fb12b0d175,过点eqId63db14a5b4334f3ea583c8fb12b0d175的直线eqId417e80f1349244878d01fe90e0891f5feqId19a4eb16029e4550a14f2afe4741a3c3交于eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6两点,若eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点,eqId9d077b0e8046474baac2bfb36c94af2b的重心为点eqIdf5119432bb364b65af514a0d221736e8,则eqId8e273238a57849d585f041be46ae2a29______
单选题 | 一般(0.65) | 2021·全国高三其他模拟(理)
解题方法
3 . 已知抛物线eqId7e148e9b5def4bf1af4353dbf1ccc544,过抛物线焦点F的直线与抛物线C交于AB两点,交抛物线的准线于点P,若FPB.中点,且eqId62c38aa49f9e46158f6a809d7d3bc8cd,则|AB|=(   )
A.eqIdd1ebfa5c81a04d18900d19595d070677B.eqIde040834dfbee4ba4aa293a5c01e4d034C.eqIdf7d6b53ad41c46fdaa1cbdb9c26ced4dD.eqIdfc5a13d488f9498bbecc6fd388b6b967
多选题 | 较难(0.4) | 2021·福建高三其他模拟
解题方法
压轴
4 . 已知抛物线eqId0acc3fc1b9f5435597cc1611b50240e0的焦点为eqIdbe692e358412467ca27ce6c9ecbfaa1f,直线eqId417e80f1349244878d01fe90e0891f5f经过点eqId63db14a5b4334f3ea583c8fb12b0d175eqId19a4eb16029e4550a14f2afe4741a3c3AeqId8754ce8cf7f34f04abb9a0c041f57f5c两点,交eqId072d7d6b911b42bc89207e72515ebf5f轴于点eqIdbedf755e0fdb4d078d6859360706b163,若eqIda181bb3b854a4eac972e85e96c14643c,则(   )
A.eqIdd7e3b20506984e1ab1448f0b85ecc137B.点eqId8754ce8cf7f34f04abb9a0c041f57f5c的坐标为eqIdc70e6e032c6b42c882b81912fb672482
C.eqIdf6845c5645d14c30bcdcdd305985a3b8D.弦eqId99a3187c2b8f4bcc9703c74c3b72f1f3的中点到eqId072d7d6b911b42bc89207e72515ebf5f轴的距离为eqIdfd383cee9c964d5b8df194d89524a147
填空题 | 一般(0.65) | 2021·四川高三三模(理)
解题方法
5 . 已知斜率为eqId317ed84d205b4156847380f7e9f38b08的直线过抛物线eqId5b3f333d2754455bb404a5f447e10f15(eqId4ab3c355d04e4aa88714d938b3fc7c74)的焦点eqId63db14a5b4334f3ea583c8fb12b0d175,与抛物线eqId93cbffaa5ae045d6ac45d1e979991c3a交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点(点eqId052844cae8574a8ab842c38a039baac0在点eqId8754ce8cf7f34f04abb9a0c041f57f5c的左侧),又eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点,点eqId19a4eb16029e4550a14f2afe4741a3c3也为抛物线eqId93cbffaa5ae045d6ac45d1e979991c3a上一点,且eqIdcf869434828e4e68b1e55ad191eab30eeqId9578172725644676915744d2c4fde057,则实数eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c的值为___________.
解答题 | 较难(0.4) | 2021·上海复旦附中高三其他模拟
解题方法
6 . 已知过点eqIdcb7b7df538764fac9b7046ac36ce8e00的直线eqId417e80f1349244878d01fe90e0891f5f与抛物线eqIdf91aad2290ad408799ceac6f8a03ae91交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,且eqId279a3f02be0e483b9f9e79268a512e34,其中eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点.
(1)求eqIdc57a748f254e4bcb825ec65d2f422fc6的值;
(2)当eqId1e34418e55644077807187a1aaed4dfe最小时,求直线eqId417e80f1349244878d01fe90e0891f5f的方程.
填空题 | 较易(0.85) | 2021·四川高三三模(文)
解题方法
典型
7 . 已知抛物线eqIdd050af449075401299cc78c647d310e8的焦点为eqId63db14a5b4334f3ea583c8fb12b0d175,过点eqId63db14a5b4334f3ea583c8fb12b0d175且斜率为eqId317ed84d205b4156847380f7e9f38b08的直线eqId417e80f1349244878d01fe90e0891f5f交抛物线于eqIdeb53cb7cb0274f7d8f111c60f824c243两点,以线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3为直径的圆交eqId072d7d6b911b42bc89207e72515ebf5f轴于eqId71891062a8724584af9a2c4c77cd566e两点,设线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3的中点为eqId8846d653e4404636a88754285c8bcb32,则eqId2e57c1bfa8ee4d8491f749fcb723a020的值为___________.
单选题 | 一般(0.65) | 2021·全国高三其他模拟
解题方法
8 . 已知斜率为k的直线l过抛物线Cy2=2pxp>0)的焦点F,与抛物线C交于AB两点,又直线l与圆x2+y2pxeqId44aff622a095465082b61837e24439e7p2=0交于CD两点.若SOABeqId8e3ab4836a874ab593bb67a2bce00575SOCD,则k的值为(  )
A.±1B.eqIda07dcb84b6f34b60885e01df357aa3d5C.eqId5a94eb2a580f4b428d481bb95bd9ecf9D.±2
填空题 | 较易(0.85) | 2021·江苏高三其他模拟
解题方法
9 . 在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,已知抛物线eqId19a4eb16029e4550a14f2afe4741a3c3eqIdd050af449075401299cc78c647d310e8的焦点为eqId63db14a5b4334f3ea583c8fb12b0d175,过点eqId63db14a5b4334f3ea583c8fb12b0d175的直线交抛物线eqId19a4eb16029e4550a14f2afe4741a3c3eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,且eqIdde920cd9ebbf461b9de3c7d24102cc1b,则eqId99a3187c2b8f4bcc9703c74c3b72f1f3的长为___________.
解答题 | 一般(0.65) |
10 . 已知抛物线eqIdd050af449075401299cc78c647d310e8的焦点为F,过点F的直线eqId417e80f1349244878d01fe90e0891f5f与该抛物线交于AB两点,Ax轴的上方,圆eqId4677430a496d48619e670b11d4e4cf43
说明: figure
(1)若eqId5ca6b76bcfe642d8874c900b49dba3ec,求点A的坐标;
(2)若直线l与圆C相切,求弦eqId99a3187c2b8f4bcc9703c74c3b72f1f3的长;
(3)若直线l与圆C交于MN两点,eqId141aacd92be1460fbdf80d5753578ae0eqId5dd61720ae9e4001a66dda87c9ee71df的面积分别记为eqIde0b0a69153d74086acac0f2b28878deceqIdc36de5c6d722440e9911d9802c4068f8,求eqId3890a25f61ac42d5a7c9934d334a7b51的取值范围.
更新:2021/06/14组卷:182
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