求数学高手抛物线y=1/3x2-(2根号3)/3x+m与x轴交与A,B两点,与y轴交与C点,∠ACB=90°(1)求m的值及抛物线顶点坐标(2过ABC三点的圆M交y轴于另一点D,连接DM并延长交圆M于点E,过E点的圆M的切线分别交
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![求数学高手抛物线y=1/3x2-(2根号3)/3x+m与x轴交与A,B两点,与y轴交与C点,∠ACB=90°(1)求m的值及抛物线顶点坐标(2过ABC三点的圆M交y轴于另一点D,连接DM并延长交圆M于点E,过E点的圆M的切线分别交](/uploads/image/z/11459913-33-3.jpg?t=%E6%B1%82%E6%95%B0%E5%AD%A6%E9%AB%98%E6%89%8B%E6%8A%9B%E7%89%A9%E7%BA%BFy%3D1%2F3x2-%EF%BC%882%E6%A0%B9%E5%8F%B73%EF%BC%89%2F3x%2Bm%E4%B8%8Ex%E8%BD%B4%E4%BA%A4%E4%B8%8EA%2CB%E4%B8%A4%E7%82%B9%2C%E4%B8%8Ey%E8%BD%B4%E4%BA%A4%E4%B8%8EC%E7%82%B9%2C%E2%88%A0ACB%3D90%C2%B0%281%29%E6%B1%82m%E7%9A%84%E5%80%BC%E5%8F%8A%E6%8A%9B%E7%89%A9%E7%BA%BF%E9%A1%B6%E7%82%B9%E5%9D%90%E6%A0%87%EF%BC%882%E8%BF%87ABC%E4%B8%89%E7%82%B9%E7%9A%84%E5%9C%86M%E4%BA%A4y%E8%BD%B4%E4%BA%8E%E5%8F%A6%E4%B8%80%E7%82%B9D%2C%E8%BF%9E%E6%8E%A5DM%E5%B9%B6%E5%BB%B6%E9%95%BF%E4%BA%A4%E5%9C%86M%E4%BA%8E%E7%82%B9E%2C%E8%BF%87E%E7%82%B9%E7%9A%84%E5%9C%86M%E7%9A%84%E5%88%87%E7%BA%BF%E5%88%86%E5%88%AB%E4%BA%A4)
求数学高手抛物线y=1/3x2-(2根号3)/3x+m与x轴交与A,B两点,与y轴交与C点,∠ACB=90°(1)求m的值及抛物线顶点坐标(2过ABC三点的圆M交y轴于另一点D,连接DM并延长交圆M于点E,过E点的圆M的切线分别交
求数学高手抛物线y=1/3x2-(2根号3)/3x+m与x轴交与A,B两点,与y轴交与C点,∠ACB=90°
(1)求m的值及抛物线顶点坐标
(2过ABC三点的圆M交y轴于另一点D,连接DM并延长交圆M于点E,过E点的圆M的切线分别交与x轴,y轴于点F,G,求直线FG的解析式
(3)上述的抛物线是否存在着点Q(a,b)使得∠DQE为钝角,存在写出横坐标a的取值范围,不存在说明理由
(4)在条件(2)下,设P为弧CBD上的动点(P不与C,D重合)连接PA交y轴于点H,问是否存在一个常数K,始终满足AH*AP=K
求数学高手抛物线y=1/3x2-(2根号3)/3x+m与x轴交与A,B两点,与y轴交与C点,∠ACB=90°(1)求m的值及抛物线顶点坐标(2过ABC三点的圆M交y轴于另一点D,连接DM并延长交圆M于点E,过E点的圆M的切线分别交
物线顶点坐标
y=(1/3)x^2-2(3^-0.5)x+m
A=(c,0),B=(d,0),C=(0,m)
(-m/c)(-m/d)=-1,m^2=-cd=-3m,m=-3
y=(1/3)x^2-2(3^-0.5)x-3=(1/3)(x^2-2(3^0.5)x+3-3)-3=(1/3)(x-3^0.5)^2-4
V=(3^0.5,-4)
M=(3^0.5,0),(x-3...
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y=(1/3)x^2-2(3^-0.5)x+m
A=(c,0),B=(d,0),C=(0,m)
(-m/c)(-m/d)=-1,m^2=-cd=-3m,m=-3
y=(1/3)x^2-2(3^-0.5)x-3=(1/3)(x^2-2(3^0.5)x+3-3)-3=(1/3)(x-3^0.5)^2-4
V=(3^0.5,-4)
M=(3^0.5,0),(x-3^0.5)^2+y^2=12
D=(0,3),Slope DM=-3^0.5,DE:y=-(3^0.5)x+3
(x-3^0.5)^2+(-(3^0.5)x+3)^2=12,x^2-2(3^0.5)x=0,E=(2(3^0.5),-3)
Slope FG=3^-0.5,FG:y=(3^-0.5)x-5
b=(1/3)(a-3^0.5)^2-4
Slope DQ=(1/3)a-2(3^-0.5)-6/a=((3^-0.5)a+2)(3^-0.5-3/a),Slope EQ=(1/3)a
a:-2(3^0.5),0,3^0.5,3^1.5
Slope DQ:0,infinity,-2(3^0.5),0
Slope EQ:-2(3^-0.5),0,3^-0.5,3^0.5
不存在
P=(e,f),e^2+f^2=12
Slope AP=f/(e+3^0.5)=(12-e^2)^0.5/(e+3^0.5)
AP:y=((12-e^2)^0.5/(e+3^0.5))x+(36-3e^2)^0.5/(e+3^0.5)
H=(0,(36-3e^2)^0.5/(e+3^0.5))
AH=(3+(36-3e^2)/(e+3^0.5)^2)^0.5=(45+2(3^0.5)e)^0.5
AP=(3+(12-e^2))^0.5=(15-e^2)^0.5
不存在
收起