Why is that,

$\displaystyle x= \sqrt{y^2 + z^2}$

Is a single cone while,

$\displaystyle x^2 = 9y^2 + z^2$

consists of 2 cones, tip to tip?

I know that the second surface consists ofellipticalcones, but I don't see how that could make any difference.

How come for,

$\displaystyle x= \sqrt{y^2 + z^2}$

my solutions manual only shows one cone? Couldn't I rewrite this as,

$\displaystyle x^{2} = y^{2} + z^{2} $

Certainly there are negative values of x that will satisfy this equation as well, right?