Answer to Question #195310 in Analytic Geometry for Ayush

Question

Identify and trace the conicoid y

2 +z

2 = x. Describe its sections by the planes

x = 0, y = 0 and z = 0.

Answer 1

It is an elliptic paraboloid:

sections by the planes

x = 0: it is only one point x=0.y=0,z=0

sections by the planes

y = 0: z² = x - it is parabola in x - z plane with x axis of symmetry

sections by the planes

z = 0: y² = x - it is parabola in x - y plane with x axis of symmetry