Question Stem for Question Nos. 17 and 18: Consider the ellipses given by x² + 4y² = 1 and 4x² + y² = 1. Let P be the point in the first quadrant where the given ellipses intersect. If θ is the acute angle between the tangents to the given ellipses at the point P, then the value of 4 tan θ is ___________.
For the Question Stem for Question Nos. 17 and 18, if α is the area of the common region that lies inside both the given ellipses, then the value of cot α is ___________.