已知抛物线
,焦点为F,准线为l,线段OF的中点为G.点P是C上在x轴上方的一点,且点P到l的距离等于它到原点O的距离.
(1)求P点的坐标.
(2)过点
作一条斜率为正数的直线
与抛物线C从左向右依次交于A,B两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1ba86ffc6e5542b62319848c14acaa.png)
(1)求P点的坐标.
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14dd75003428d5b4071aabbaa4d11cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c443f5fc06491a7f1fdd470467cc5581.png)
更新时间:2022-11-14 14:49:13
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【推荐1】已知F是抛物线
的焦点,
是抛物线上一点,且
.
(1)求抛物线C的方程;
(2)斜率为1的且过焦点的直线
与抛物线C交于A,B两点,求△PAB的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1d86b13064d4002a55a99131d38741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0a0328dde917c3e6d0f1ca9ddb6027b.png)
(1)求抛物线C的方程;
(2)斜率为1的且过焦点的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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【推荐2】抛物线
的焦点为
,准线为
,在其上取一点
,以
为圆心,
为半径的圆
交准线
于
,
两点.
(1)若
,
的面积为
,求抛物线的方程及圆
的方程;
(2)若
,
,
三点在同一直线
上,直线
与
平行,且
与
相切,已知直线
被以
为圆心,
为半径的圆
截得的弦长为
,求抛物线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf92a1ba410263d4f68b7e0432b19aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a477603f3f88c3b48352b6130f9ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc66f2d099e9f18f653f39e4f4157fdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a477603f3f88c3b48352b6130f9ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8135c86c2bec5297961a6e5e7cd50e56.png)
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【推荐1】如图,在平面直角坐标系xOy中,已知直线l:x-y-2=0,抛物线C:y2=2px(p>0).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/9/5d847ad6-afa3-45cf-8d15-879a4f1e9870.png?resizew=122)
(1)若直线l过抛物线C的焦点,求抛物线C的方程;
(2)当p=1时,若抛物线C上存在关于直线l对称的相异两点P和Q.求线段PQ的中点M的坐标.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/9/5d847ad6-afa3-45cf-8d15-879a4f1e9870.png?resizew=122)
(1)若直线l过抛物线C的焦点,求抛物线C的方程;
(2)当p=1时,若抛物线C上存在关于直线l对称的相异两点P和Q.求线段PQ的中点M的坐标.
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【推荐2】已知点
到直线
的距离等于
,其中
.设平面内与点F和直线
距离相等的点的轨迹为C.
(1)求C的方程;
(2)设
与C在第一象限的交点为A,
与x轴的交点为B,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f6d06b9a4d3a891ea7c986b1ab4e925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7c90d155f309e54303f68d91a6b5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a4c25fa7b7754fc55548e2497a9d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0bae54510610d3118cc785489001096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc3624ac3279fa0d23e45c6259f1864.png)
(1)求C的方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
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【推荐1】已知点F为抛物线C:y2=4x的焦点,过点F作斜率为k的直线l与抛物线交于A,B两点,与准线交于点P,设点D为抛物线准线与x轴的交点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/7eef7ec7-a141-4f27-a86f-c86fb0cff2e0.png?resizew=150)
(1)若k=﹣1,求△DAB的面积;
(2)若
λ
,
μ
,证明:λ+μ为定值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/7eef7ec7-a141-4f27-a86f-c86fb0cff2e0.png?resizew=150)
(1)若k=﹣1,求△DAB的面积;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b59d7dc1a0603a0379445fafeb376c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc3fe4dd2a5fec23164d424ea9a229f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6dae7f88dbc703ba104467f6e1a323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60442f1d2e0ec6b40594e3e810949543.png)
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【推荐2】在平面直角坐标系中,已知点
,点B在直线
:
上运动,过点B与
垂直的直线和线段AB的垂直平分线相交于点M.
(1)求动点M的轨迹E的方程;
(2)过(1)中轨迹E上的点P (1,2)作两条直线分别与轨迹E相交于
,
两点.试探究:当直线PC,PD的斜率存在且倾斜角互补时,直线CD的斜率是否为定值?若是,求出这个定值;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6ff81aedbefa935da289dc632e78eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求动点M的轨迹E的方程;
(2)过(1)中轨迹E上的点P (1,2)作两条直线分别与轨迹E相交于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5e40f31633a3444bfde7187b0808774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/863226efe54b4273103415677e5de2f7.png)
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