The point, at which the maximum value of $10 x+6 y$ subject to the constraints $x+y \leq 12$, $2 x+y \leq 20, x \geq 0, y \geq 0$ occurs, is

If the line $\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z+4}{3}$ lies in the plane $\ell x+m y-z=9$, then $\ell^2+m^2$ is

The mean of 100 observations is 50 and their standard deviation is 5 , then the sum of all squares of all the observations is

The area of the region bounded by hyperbola $x^2-y^2=9$ and its latus rectum is