x^2/16+y^2/9=1,A,B是椭圆上两点,A,B的垂直平分线与X轴交于p(x0,0),求x0的取值范围.-7/4
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![x^2/16+y^2/9=1,A,B是椭圆上两点,A,B的垂直平分线与X轴交于p(x0,0),求x0的取值范围.-7/4](/uploads/image/z/6931293-69-3.jpg?t=x%5E2%2F16%2By%5E2%2F9%3D1%2CA%2CB%E6%98%AF%E6%A4%AD%E5%9C%86%E4%B8%8A%E4%B8%A4%E7%82%B9%2CA%2CB%E7%9A%84%E5%9E%82%E7%9B%B4%E5%B9%B3%E5%88%86%E7%BA%BF%E4%B8%8EX%E8%BD%B4%E4%BA%A4%E4%BA%8Ep%EF%BC%88x0%2C0%29%2C%E6%B1%82x0%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.-7%2F4)
x^2/16+y^2/9=1,A,B是椭圆上两点,A,B的垂直平分线与X轴交于p(x0,0),求x0的取值范围.-7/4
x^2/16+y^2/9=1,A,B是椭圆上两点,A,B的垂直平分线与X轴交于p(x0,0),求x0的取值范围.
-7/4
x^2/16+y^2/9=1,A,B是椭圆上两点,A,B的垂直平分线与X轴交于p(x0,0),求x0的取值范围.-7/4
设A(x1,y1),B(x2,y2),设直线AB的中点为点D,
点D的坐标为((x1+x2)/2,(y1+y2)/2),
直线AB的斜率为,(y2-y1)/(x2-x1)
直线DP的斜率为,k=-(x2-x1)/ (y2-y1)
直线DP的方程为y-(y1+y2)/2=-[(x2-x1)/ (y2-y1)]*(x-(x1+x2)/2)
0-(y1+y2)/2=-[(x2-x1)/ (y2-y1)]*(x0-(x1+x2)/2)
(y1+y2)/2=[(x2-x1)/ (y2-y1)]*(x0-(x1+x2)/2)
(y2^2-y1^2)/ [2(x2-x1)]= x0-(x1+x2)/2
X0=(y2^2-y1^2)/ [2(x2-x1)]+ (x1+x2)/2
=1/2[(y2^2-y1^2)+ (x2^2-x1^2)]/ (x2-x1)
X1^2/16+y1^2/9=1, X2^2/16+y2^2/9=1,两式相减
(y2^2-y1^2)/9+(x2^2-x1^2)/16=0
(y2^2-y1^2)=-9(x2^2-x1^2)/16
X0=1/2[(y2^2-y1^2)+ (x2^2-x1^2)]/ (x2-x1)
=1/2[7(x2^2-x1^2)/16] / (x2-x1)
=(7/16)*(x1+x2)/2
(x1+x2)/2是点D的横坐标,点D在椭圆内部,-4