已知直线y=k(x-2)与抛物线y=x^2交于AB两点,求线段AB中点M的轨迹方程
问题描述:
已知直线y=k(x-2)与抛物线y=x^2交于AB两点,求线段AB中点M的轨迹方程
答
y=k(x-2),y = x²x² = k(x - 2)x² - kx + 2k = 0x₁ + x₂ = kM(x,y)x = (x₁ + x₂)/2 = k/2,k = 2x (1)y = (y₁ + y₂)/2 = [k(x₁ - 2) + k(x₂ - 2)]/2 ...