Answer to Question #91545 in Analytic Geometry for Ra

Question

Identify and trace the conicoid y²+z²=x. Describe its sections by the planes x=0, y=0 and z=0.

Answer 1

This is an example of elliptical paraboloid.

General equation of elliptical paraboloid is

z= x²+y²

Here the equation is given as

z²+y²=x

Which passes through origin (as it's vertex)

And is a parabola lying upward.

When Plane X=0

Put the value of X in the equation

X=z²+y²

0=z²+y²

Which implies y=0;z=0 which is origin itself.

When y=0

The conicoid reduces to z²=x which is a parabola having symmetry along X axis in x-z plane.

When z= 0

The conicoid reduces to y²=x which is also a parabola having symmetry along X axis in x-y plane.