Consider the ellipse\( \dfrac{x^2}{4} + \dfrac{y^2}{3} = 1. \)
Let \( H(\alpha, 0) \), \( 0 < \alpha < 2 \), be a point. A straight line drawn through \( H \) parallel to the \( y -\)axis crosses the ellipse and its auxiliary circle at points \( E \) and \( F \) respectively, in the first quadrant. The tangent to the ellipse at the point \( E \) intersects the positive \( x \)-axis at a point \( G \). Suppose the straight-line joining \( F \) and the origin makes an angle \( \phi \) with the positive \( x -\)axis.
The correct option is:
