X2+Y2+10X-24=0 X2+Y2-10X+24=0都相切的圆的圆心轨迹
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![X2+Y2+10X-24=0 X2+Y2-10X+24=0都相切的圆的圆心轨迹](/uploads/image/z/6924751-7-1.jpg?t=X2%2BY2%2B10X-24%3D0+X2%2BY2-10X%2B24%3D0%E9%83%BD%E7%9B%B8%E5%88%87%E7%9A%84%E5%9C%86%E7%9A%84%E5%9C%86%E5%BF%83%E8%BD%A8%E8%BF%B9)
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X2+Y2+10X-24=0 X2+Y2-10X+24=0都相切的圆的圆心轨迹
X2+Y2+10X-24=0 X2+Y2-10X+24=0都相切的圆的圆心轨迹
X2+Y2+10X-24=0 X2+Y2-10X+24=0都相切的圆的圆心轨迹
X2+Y2+10X-24=0化为(X+5)2+Y2=49
则其圆心为(-5,0)
X2+Y2-10X+24=0化为X2+(Y-5)2=1
则其圆心为(0,5)半径为1
假设和她们相切的圆的圆心为(x,y)半径为r
则有
√[(x+5)2+y2]=r+7
√[x2+(y-5)2]=r+1
把r消去就可以了
设圆半径r
到(x+5)2+y2=49圆心的距离d1为r+7
到(x-5)2+y2=1圆心的距离d2为r+1
d1-d2=6
即轨迹为以(-5,0)(5,0)为焦点,长轴为8的椭圆。