If the director circle of ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ of eccentricity $\frac{1}{\sqrt{3}}$ passes through the two foci of the hyperbola $H:\frac{y^2}{9}-\frac{x^2}{16}=1$ then:

Area of square formed by four tangents to ellipse $E$ is 50 sq. units.

Number of points on ellipse from which two perpendicular tangents can be drawn to hyperbola $H$ is 4.

Area of quadrilateral formed by tangents at ends of latus rectum of ellipse $E$ is $30\sqrt{3}$ sq. units.

Equation of director circle of ellipse is $x^2+y^2=25.$