Question

What surface is represented by x^2+y^2=9z? Give a rough sketch of it. Obtain the section of this surface by the plane y=0.

Answer 1

$\dfrac{x^2}{9} +\dfrac{y^2}{9} = z\\ {(\dfrac{x}{3})}^2 +{(\dfrac{y}{3})}^2 = z\\$

This is an elliptical paraboloid.

The section of the plane y=0 is the parabola

$x^2 = 9z$