Conic Sections

Consider the ellipse E given by x218+ y212=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 5 y=x2 in the first quadrant. Let d be the distance between P and Q. If a and b are the integers such that d2=a+b 5, then the value of a-b is .