Question

高中数学问题求解

Answer 1

x² = 8(y - 1) = 8[px + (1 - 2p²) - 1] = 8px - 16p²

x² - 8px + 16p² = (x - 4p)² = 0
this means that their shared points are the same

Let the gradient be k, the tangent is y + 7 = k(x - 0), y = kx - 7
x² = 8(y - 1) = 8(kx - 7 - 1) = 8kx - 64
x² - 8kx + 64 = 0
For it to be in the form of (x + t)² = 0, t must be ±8
when t = 8, (x + 8)² = x² + 16x + 64 = 0, -8k = 16, k = -2
when t = -8, (x - 8)² = x² - 16x + 64 = 0, -8k = -16, k = 2