Answer
$z=\frac{1}{5}(x^2+y^2)$
Work Step by Step
Step 1. Write the general form as $z=k(x^2+y^2)$ where $k$ is a constant.
Step 2. Use the given condition, $5=k(3^2+4^2)$, thus $k=\frac{1}{5}$
Step 3. We have $z=\frac{1}{5}(x^2+y^2)$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.