Answer
Please see the figure attached.
Work Step by Step
The contour map of $f\left( {x,y} \right) = {x^2} + 4{y^2}$ with level curves $c = 1,4,7,...,16$ is obtained by plotting the curves:
$c = {x^2} + 4{y^2}$ for $c = 1,4,7,...,16$
The contour interval: $m=3$.
