如图,抛物线y=ax²+bx+c(a,b,c是常数,a≠0)的对称轴为y轴,且经过（0,0

如图,抛物线y=ax²+bx+c(a,b,c是常数,a≠0)的对称轴为y轴,且经过（0,0

过(0,0),x = 0,y = c = 0y = ax² + bx对称轴为y轴:x = -b/(2a) = 0,b = 0y = ax²x = √a,y = a² = 1/16,a = 1/4 (舍去a = -1/4,此时抛物线不可能在x轴上方)y = x²/4P(p,p²/4),圆P为(x - p)² + (y - p²/4)² = r²x = 0,y = 2,r² = p² + (2 - p²/4)²(x - p)² + (y - p²/4)² = p² + (2 - p²/4)²圆心P与x轴的距离为d = p²/4r² - d² = p² + (2 - p²/4)² - (p²/4)² = p² + (2 - p²/4 + p²/4)(2 - p²/4 - p²/4)= p² + 2(2 - p²/2)= 4 > 0圆总与x轴相交圆P 可以变为(x - p)² + y² - p²y/2 = 4令y = 0,(x - p)² = 4x = 2 + p或x = -2 + pM(-2 + p,0),N(2 + p,0),A(0,2)(i) AM = ANA须在MN的中垂线上,p = 0,P(0,0)(ii) MA＝ MN(p - 2 - 0)² + (0 - 2)² = (p + 2 - p + 2)²p = 2 ±2√3,P(2 ±2√3,4 ±2√3)(iii) NA = NM结果与(ii)相同.

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