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

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

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

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