Let \(\theta\) be the acute angle between the tangents to the ellipse \(\frac{x^2}{9}+\frac{y^2}{1}=1\) and the circle \…

Let \(\theta\) be the acute angle between the tangents to the ellipse \(\frac{x^2}{9}+\frac{y^2}{1}=1\) and the circle \(x^2+y^2=3\) at their point of intersection in the first quadrant. The \(\tan \theta\) is equal to:

[JEE Main 2021, 1 Sep (Shift 2)]