Hyperbola and Ellipse Common Tangent
For the hyperbola
H:x2−y2=1 and the ellipse
E:+=1,a>b>0, let the
(1) eccentricity of
E be reciprocal of the eccentricity of
H, and
(2) the line
y=√x+K be a common tangent of
F and
H.
Then
4(a2+b2) is equal to ________.