1.
y² = 8x,= 2px,p = 4,焦点(2,0); a = 2
离心率e,e² = 3/4 = c²/a² = (a² - b²)/a² = 1 - b²/4
b² = 1
椭圆:x²/4 + y² = 1
2.
直线L:y - √2 = k(x - 0),y = kx + √2
带入椭圆:(4k² + 1)x² + 8√2kx + 4 = 0
x₁ + x₂ = -8√2k/(4k² + 1)
线段PQ的中点横坐标 = (x₁ + x₂)/2 = -4√2k/(4k² + 1) = -4√2/5
k/(4k² + 1) = 1/5
4k² - 5k + 1 = (4k - 1)(k - 1) = 0
k = 1/4 (请自己验证,此时无交点,舍去)
k = 1,y = x + √2