Question

Find the equation of the intersection of the surface z=4-y2 with the x-y plane.

(a) y=2

(b) y=+3, y=-3

(c) y=+4, y=-4

(d) y=+2, y=-2

I got this question during an interview.

This intriguing question originated from Intersection of Surfaces in chapter Development of Surfaces, Isometric Projections, Perspective Projections & Transformation of Projections of Civil Engineering Drawing

Answer 1

Correct choice is (d) y=+2, y=-2

Explanation: Set z = 0 in the equation, you get 0 = 4-y^2. That simplifies to y^2 = 4, or y = ±2, i.e. two lines: y = 2 and y = -2.