已知点M（1,y）在抛物线C:y²=2px（p>0）上,M点到抛物线的焦点距离为2,直线l:y=－1/2x+b与抛物线交

抛物线C:y²=2px的准线为 x = -p/2, M到准线的距离为1 - (-p/2) = 1 +p/2 = 2, p = 2
y = -x/2 + b
(-x/2 + b)² = 4x
x² - 4(b+4)x + 4b² = 0
x₁ + x₂ = 4(b + 4)
x₁x₂ = 4b²
AB的中点的横坐标为c = (x₁ + x₂)/2 = 2(b+4)
圆与x轴相切, c为圆的半径, 直径d = 4(b+4)
直径d² = AB² = (x₁ - x₂)² + (y₁ - y₂)²
= (x₁ - x₂)² + (-x₁/2 + b + x₂/2 - b)²
= (5/4)(x₁ - x₂)²
= (5/4)[(x₁ + x₂)² - 4x₁x₂]
= (5/4)[16(b + 4)² - 16b²]
= 160(b + 2)
= [4(b + 4)]²
b = 1 ± √5
圆心E(2(5 ± √5), -4)
圆的方程: [x - 2(5 ± √5)]² + (y + 4)² = 4(5 ± √5)²