If  $e_1$ and $e_2$ are the eccentricities of the ellipse, $\frac{x^2}{18}+\frac{y^2}{4}=1$ and the hyperbola, $\frac{x^2}{9}-\frac{y^2}{4}=1$  respectively and $(e_1,e_2)$ is a point on the ellipse, $15x^2+3y^2=k$ , then k is equal to

Eccentricity of ellipse,  $e_1=\sqrt{1-\frac{4}{18}}=\sqrt{\frac{7}{9}}=\frac{\sqrt{7}}{3}$
Eccentricity of hyperbola,  $e_2=\sqrt{1+\frac{4}{9}}=\sqrt{\frac{13}{9}}=\frac{\sqrt{13}}{3}$
Since, the point $(e_1,e_2)$ is on the ellipse
$15x^2+3y^2=k$  
Then,  $15e_1^2+3e_2^2=k$
 $\Rightarrow k=15\left(\frac{7}{9}\right)+3\left(\frac{13}{9}\right)$
 $\Rightarrow k=16$