Consider the ellipse \( E \) given by \( \frac{x^2}{18} + \frac{y^2}{12} = 1 \). Let \( H \) be the hyperbola whose eccentricity is the reciprocal of the eccentricity of \( E \) and whose foci are the same as that of \( E \). Let \( P \) and \( Q \) be the points of intersection of \( H \) and the parabola \( \sqrt{5}\,y = x^2 \) in the first quadrant. Let \( d \) be the distance between \( P \) and \( Q \).
