1过点A(3,-1)且被该点平分的双曲线x^2/4-y^2=1的弦所在直线的方程是抛物线y^2=x上存在不同两点AB关于直线y=k(x-1)+1对称则k的取值范围是2已知A,B是抛物线x^2=(1/a)y(a>0)上两点,O为原点,OA垂直于OB,
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![1过点A(3,-1)且被该点平分的双曲线x^2/4-y^2=1的弦所在直线的方程是抛物线y^2=x上存在不同两点AB关于直线y=k(x-1)+1对称则k的取值范围是2已知A,B是抛物线x^2=(1/a)y(a>0)上两点,O为原点,OA垂直于OB,](/uploads/image/z/14274530-26-0.jpg?t=1%E8%BF%87%E7%82%B9A%283%2C-1%29%E4%B8%94%E8%A2%AB%E8%AF%A5%E7%82%B9%E5%B9%B3%E5%88%86%E7%9A%84%E5%8F%8C%E6%9B%B2%E7%BA%BFx%5E2%2F4-y%5E2%3D1%E7%9A%84%E5%BC%A6%E6%89%80%E5%9C%A8%E7%9B%B4%E7%BA%BF%E7%9A%84%E6%96%B9%E7%A8%8B%E6%98%AF%E6%8A%9B%E7%89%A9%E7%BA%BFy%5E2%3Dx%E4%B8%8A%E5%AD%98%E5%9C%A8%E4%B8%8D%E5%90%8C%E4%B8%A4%E7%82%B9AB%E5%85%B3%E4%BA%8E%E7%9B%B4%E7%BA%BFy%3Dk%28x-1%29%2B1%E5%AF%B9%E7%A7%B0%E5%88%99k%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E6%98%AF2%E5%B7%B2%E7%9F%A5A%2CB%E6%98%AF%E6%8A%9B%E7%89%A9%E7%BA%BFx%5E2%3D%EF%BC%881%2Fa%EF%BC%89y%28a%3E0%29%E4%B8%8A%E4%B8%A4%E7%82%B9%2CO%E4%B8%BA%E5%8E%9F%E7%82%B9%2COA%E5%9E%82%E7%9B%B4%E4%BA%8EOB%2C)
1过点A(3,-1)且被该点平分的双曲线x^2/4-y^2=1的弦所在直线的方程是抛物线y^2=x上存在不同两点AB关于直线y=k(x-1)+1对称则k的取值范围是2已知A,B是抛物线x^2=(1/a)y(a>0)上两点,O为原点,OA垂直于OB,
1过点A(3,-1)且被该点平分的双曲线x^2/4-y^2=1的弦所在直线的方程是
抛物线y^2=x上存在不同两点AB关于直线y=k(x-1)+1对称则k的取值范围是
2已知A,B是抛物线x^2=(1/a)y(a>0)上两点,O为原点,OA垂直于OB,则线段AB中点M的轨迹方程是
3与纵轴及圆x^2+y^2=R^2(R>0)都相切的动圆圆心的轨迹方程是
4已知圆O1(x-5)^2+y^2=100圆O2(x+5)^2+y^2=16 这和这两个圆一个内切一个外切的动圆圆心的轨迹方程是
5以椭圆x^2/100+y^2/75=1右焦点为圆心且与双曲线x^2/9-y^2/16=1的渐近线相切的圆方程为
1过点A(3,-1)且被该点平分的双曲线x^2/4-y^2=1的弦所在直线的方程是抛物线y^2=x上存在不同两点AB关于直线y=k(x-1)+1对称则k的取值范围是2已知A,B是抛物线x^2=(1/a)y(a>0)上两点,O为原点,OA垂直于OB,
第一题:
直线经过点M(3,-1),则设所求的直线方程为:
y+1=k(x-3),即y=kx-3k-1
解下方程组:
y=kx-3k-1.(1)
x^2/4-y^2=1.(2)
即可得弦与双曲线的交点坐标:
x^2/4-(kx-3k-1)^2=1
(0.25-k^2)x^2+2k(3k+1)x-(3k+1)^2-1=0
x1+x2=-2k(3k+1)/(0.25-k^2)
因为x1、x2是弦与双曲线x^2/4-y^2=1两个交点的横坐标,由已知条件可知,点M(3,-1)为弦的中点,则
(x1+x2)/2=-k(3k+1)/(0.25-k^2)=3
k=-0.75
直线方程:y=-0.75x+1.25,即3x+4y-5=0
第五题:
椭圆x^2/100+y^2/75=1的右焦点为(5,0)
双曲线x^2/9-y^2/16=1的渐近线L为y=±(4/3)x
点(5,0)到L距离为(5*4+0)/5=4
∴R=4
∴方程为(x-5)^2+y^2=16