Question

The tangents are drawn to the ellipse $\frac{x^2}{9}+\frac{y^2}{5}=1$ at the ends of latus rectum. The area of the quadrilateral formed is

Answer 1

$\begin{array}{c}\frac{x^2}{9}+\frac{y^2}{5}=1\\ tangentsequation\pm y=\pm \frac{6}{5}x+c\\ distanceof1sideofparallelogram\\ \Rightarrow a=\frac{612}{90}\\ \Rightarrow area=\frac{4\times 612}{90}=165.37Ans.\end{array}$