MathematicsMedium57×since 2003Q3982Let H:−x2a2+y2b2=1H: \frac{-x^2}{a^2}+\frac{y^2}{b^2}=1H:a2−x2+b2y2=1 be the hyperbola, whose eccentricity is 3\sqrt{3}3 and the length of the latus rectum is 434 \sqrt{3}43. Suppose the point (α,6),α>0(\alpha, 6), \alpha>0(α,6),α>0 lies on HHH. If β\betaβ is the product of the focal distances of the point (α,6)(\alpha, 6)(α,6), then α2+β\alpha^2+\betaα2+β is equal toA170B171C169D172Check answerSkip