点M(x,y)为抛物线y^2=4x上的动点,A(a,0)为定点,求|MA|的最小值.
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点M(x,y)为抛物线y^2=4x上的动点,A(a,0)为定点,求|MA|的最小值.
点M(x,y)为抛物线y^2=4x上的动点,A(a,0)为定点,求|MA|的最小值.
点M(x,y)为抛物线y^2=4x上的动点,A(a,0)为定点,求|MA|的最小值.
|MA|²=(x-a)²+y²=(x-a)²+4x=x²-(2a-4)x+a²=(x-a+2)²+4a+4
对称轴为x=a-2,点M中,x>=0
所以a-2=0时,当x=a-2时,|MA|²最小,最小值为4a+4
所以a=2时,|MA|最小为2√(a+1)