圆心在抛物线x^2=2y 上,并且与抛物线的准线及y轴都相切的圆的方程A:x^2+y^2-x-2y-1/4=0B:x^2+y^2+x-2y+1=0C:x^2+y^2-x-2y=0D:x^2+y^2-2x-y+1/4=0
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![圆心在抛物线x^2=2y 上,并且与抛物线的准线及y轴都相切的圆的方程A:x^2+y^2-x-2y-1/4=0B:x^2+y^2+x-2y+1=0C:x^2+y^2-x-2y=0D:x^2+y^2-2x-y+1/4=0](/uploads/image/z/2798472-48-2.jpg?t=%E5%9C%86%E5%BF%83%E5%9C%A8%E6%8A%9B%E7%89%A9%E7%BA%BFx%5E2%3D2y+%E4%B8%8A%2C%E5%B9%B6%E4%B8%94%E4%B8%8E%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%9A%84%E5%87%86%E7%BA%BF%E5%8F%8Ay%E8%BD%B4%E9%83%BD%E7%9B%B8%E5%88%87%E7%9A%84%E5%9C%86%E7%9A%84%E6%96%B9%E7%A8%8BA%3Ax%5E2%2By%5E2-x-2y-1%2F4%3D0B%3Ax%5E2%2By%5E2%2Bx-2y%2B1%3D0C%3Ax%5E2%2By%5E2-x-2y%3D0D%3Ax%5E2%2By%5E2-2x-y%2B1%2F4%3D0)
圆心在抛物线x^2=2y 上,并且与抛物线的准线及y轴都相切的圆的方程A:x^2+y^2-x-2y-1/4=0B:x^2+y^2+x-2y+1=0C:x^2+y^2-x-2y=0D:x^2+y^2-2x-y+1/4=0
圆心在抛物线x^2=2y 上,并且与抛物线的准线及y轴都相切的圆的方程
A:x^2+y^2-x-2y-1/4=0
B:x^2+y^2+x-2y+1=0
C:x^2+y^2-x-2y=0
D:x^2+y^2-2x-y+1/4=0
圆心在抛物线x^2=2y 上,并且与抛物线的准线及y轴都相切的圆的方程A:x^2+y^2-x-2y-1/4=0B:x^2+y^2+x-2y+1=0C:x^2+y^2-x-2y=0D:x^2+y^2-2x-y+1/4=0
准线:y=-1/2
设圆心坐标(x,x^2/2)
则:|x|=x^2/2+1/2
x^2-2|x|+1=0
(|x|-1)^2=0
|x|=1
x=±1
圆心坐标(±1,1/2)
半径= |x|=1
所以,所求圆方程为:
(x-1)^2+(y-1/2)^2=1
或,(x+1)^2+(y-1/2)^2=1
设圆心(x,1/2(x^2)) ,半径r
因为抛物线准线为y=-1/2
{
1/2(x^2)+1/2=r (圆心到准线距离等于半径)
|x|=r (圆心到y轴距离等于半径
}
解得x=+/-1,r=1
所以该圆为圆心是(+/-1,1/2)半径为1的圆
∵y²=2x 所以准线为x=-2/4=-1/2(1)P(x,√2x)是抛物线在x轴上部的点,若此点满足题意则有√2x=x+|-1/2| 2x=x²+x+1/4 解得x=1/2所以y=√(2×1/2)=1 r=x+1/2=1 圆的方程为(x-1/2)²+(y-1)²=1(2)P(x,-√2x)是抛物线在x轴下部的点,若此点满足题意则有|-√2x|=x+|...
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∵y²=2x 所以准线为x=-2/4=-1/2(1)P(x,√2x)是抛物线在x轴上部的点,若此点满足题意则有√2x=x+|-1/2| 2x=x²+x+1/4 解得x=1/2所以y=√(2×1/2)=1 r=x+1/2=1 圆的方程为(x-1/2)²+(y-1)²=1(2)P(x,-√2x)是抛物线在x轴下部的点,若此点满足题意则有|-√2x|=x+|-1/2| 2x=x²+x+1/4 解得x=1/2所以y=-√(2×1/2)=-1 r=|-√2x|=1 圆的方程为(x-1/2)²+(y+1)²=1
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