#59 · Functions & graphs · Class 12
Paraboloid Surface
A bowl-shaped surface z = k(x² + y²). Every horizontal cut is a circle; every vertical cut through the axis is a parabola.
Paraboloid Surface📐 Formula
z = k(x² + y²); at radius ρ the height is kρ²
✏️ Worked example
k = 0.25: at ρ = 2, z = 1.
🌍 Where it is used
Satellite dishes and telescope mirrors focus rays at one point.
❓ Quick check
Horizontal cross-sections of z = x² + y² are…