Question

Find the minimum distance between the origin and the
surface x^2y - z^2 + 9 = 0.

Answer 1

`x = + - \sqrt{ \frac{z {}^(2) - 9 }{y}}`

Explanation:

`1. \: x {}^(2) y + 9 = z {}^(2) \\ 2. \: x {}^(2) = z {}^(2) - 9 \\ 3. \: x {}^(2) = \frac{z {}^(2) - 9}{y} \\ 4. \: x = + - \sqrt{ \frac{z {}^(2) - 9 }{y}}`