MathNet 2006 — Part 04 Question 108

Let $F_{1}$ and $F_{2}$ be the foci of the ellipse $4 x^{2}+9 y^{2}=36$ and $K$ a point on this ellipse such that $\left|K F_{1}\right| : \left|K F_{2}\right|=2: 1$. Calculate the area of ​​the triangle $K F_{1} F_{2}$.