(1) 焦點(diǎn)F1(-c, 0), F2(c, 0); 上頂點(diǎn)B2(0, b)
向量F1B2 = (c, b), 向量F2B = (-c, b)
F1B2⊥ F2B2, 向量F1B2•向量F2B2 = -c² + b² = 0, b = c
直線l: y = x - b
代入x² = 4y, x² = 4(x - b), x² - 4x + 4b = 0
∆ = 16 - 16b = 0
b = 1, c = 1
a² = b² + c² = 2
橢圓的方程: x²/2 + y² = 1
(2)
直線l: y = x - 1
代入橢圓的方程: x²/2 + (x - 1)² = 1
x(3x - 4) = 0
x = 0, B(0, -1)
x = 4/3, A(4/3, 1/3)
向量OA + 向量OB = (4/3, -2/3)
向量OP = -(向量OA + 向量OB) = (-4/3, 2/3), P(-4/3, 2/3)
代入橢圓的方程: (-4/3)²/2 + (2/3)² = 8/9 + 4/9 = 4/3 ≠ 1
P不在橢圓C上