Question

Describe the level surface of the function\(f\left( {x,y,z} \right) = {x^2} + 3{y^2} + 5{z^2}\).

Short answer

Answer is not given in the drive

Step-by-step solution

Level curves: \(f\left( {x,y} \right) = k\)

So,

\(\begin{aligned}{l}f\left( {x,y,z} \right) &= k\\{x^2} + 3{y^2} + 5{z^2} &= k\end{aligned}\) (Here\(K \ge 0\))

These are family of ellipsis for\(K > 0\)and this is origin if\(K = 0\).