不妨取顶点A(a,0),渐近线y = bx/a,bx - ay = 0
距离为d = |ab - a*0|/√(a² + b²) = ab/c =√2c/3
ab/c² = √2/3 = [a√(c² - a²)]/c² = √(c² - a²)/(c*c/a) = √(1 - a²/c²)/(c/a)
= √(1 - 1/e²)/e
2e²/9 = 1 - 1/e²
2e⁴ - 9e² + 9 = 0
(2e² - 3)(e² - 3) = 0
e² = 3/2(e = √6/2) 或e² = 3 (e= √3)