一道参数题目已知设直线l:x=4+t*cos(a),y=-2+t*sin(a)(t为参数,a为倾斜角)与椭圆:x^2/4+y^2=1相交与不同两点M,N.已知点P坐标为(4,-2).(1)求PM*PN的取值范围(2)设点Q为直线上一点,且满足2/(PQ)=1/(PM)+1/(PN
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![一道参数题目已知设直线l:x=4+t*cos(a),y=-2+t*sin(a)(t为参数,a为倾斜角)与椭圆:x^2/4+y^2=1相交与不同两点M,N.已知点P坐标为(4,-2).(1)求PM*PN的取值范围(2)设点Q为直线上一点,且满足2/(PQ)=1/(PM)+1/(PN](/uploads/image/z/10156256-8-6.jpg?t=%E4%B8%80%E9%81%93%E5%8F%82%E6%95%B0%E9%A2%98%E7%9B%AE%E5%B7%B2%E7%9F%A5%E8%AE%BE%E7%9B%B4%E7%BA%BFl%3Ax%3D4%2Bt%2Acos%28a%29%2Cy%3D-2%2Bt%2Asin%28a%29%EF%BC%88t%E4%B8%BA%E5%8F%82%E6%95%B0%2Ca%E4%B8%BA%E5%80%BE%E6%96%9C%E8%A7%92%EF%BC%89%E4%B8%8E%E6%A4%AD%E5%9C%86%3Ax%5E2%2F4%2By%5E2%3D1%E7%9B%B8%E4%BA%A4%E4%B8%8E%E4%B8%8D%E5%90%8C%E4%B8%A4%E7%82%B9M%2CN.%E5%B7%B2%E7%9F%A5%E7%82%B9P%E5%9D%90%E6%A0%87%E4%B8%BA%284%2C-2%29.%281%29%E6%B1%82PM%2APN%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%EF%BC%882%EF%BC%89%E8%AE%BE%E7%82%B9Q%E4%B8%BA%E7%9B%B4%E7%BA%BF%E4%B8%8A%E4%B8%80%E7%82%B9%2C%E4%B8%94%E6%BB%A1%E8%B6%B32%2F%28PQ%29%3D1%2F%28PM%29%2B1%2F%28PN)
一道参数题目已知设直线l:x=4+t*cos(a),y=-2+t*sin(a)(t为参数,a为倾斜角)与椭圆:x^2/4+y^2=1相交与不同两点M,N.已知点P坐标为(4,-2).(1)求PM*PN的取值范围(2)设点Q为直线上一点,且满足2/(PQ)=1/(PM)+1/(PN
一道参数题目
已知设直线l:x=4+t*cos(a),y=-2+t*sin(a)(t为参数,a为倾斜角)与椭圆:x^2/4+y^2=1相交与不同两点M,N.已知点P坐标为(4,-2).
(1)求PM*PN的取值范围
(2)设点Q为直线上一点,且满足2/(PQ)=1/(PM)+1/(PN).当a变化时,求点Q的轨迹方程(答案如完整则会加悬赏值)
一道参数题目已知设直线l:x=4+t*cos(a),y=-2+t*sin(a)(t为参数,a为倾斜角)与椭圆:x^2/4+y^2=1相交与不同两点M,N.已知点P坐标为(4,-2).(1)求PM*PN的取值范围(2)设点Q为直线上一点,且满足2/(PQ)=1/(PM)+1/(PN
(1)显然,点P在直线L上,|t|的几何意义是直线L上的点到点P的距离.
联立直线方程与圆方程:(4+t*cos(a))^2/4+(-2+t*sin(a))^2=1,
化简得:(1-3/4*cos(a)^2)*t^2+(2*cos(a)-4*sin(a))*t+7,……①
这是一个关于t的二次方程.
由于直线与椭圆交于两个不同点,故判别式Δ>0,即
(2*cos(a)-4*sin(a))^2-4*7*(-3/4*cos(a)^2+1)>0,
化简得:9*cos(a)^2-16*cos(a)*sin(a)-12>0,
即:-3*cos(a)^2-16*cos(a)*sin(a)-12*sin(a)^2>0,
3*cos(a)^2+16*cos(a)*sin(a)+12*sin(a)^2