TS EAMCET 03 May 2019 Shift 1 Solved Paper

A line perpendicular to the X-axis cuts the circle x2+y2 = 9 at A and the ellipse 4x2+9y2 = 36 at B such that A and B lie in the same quadrant. If θ is the greatest acute angle between the tangents drawn to the curves at A and B, then tan θ =