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51.

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=-2I 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

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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.
Discussion
52.

The nature of surface of sphere is ______________(a) plane surface(b) singly curved surface(c) singly or doubly curved surface(d) doubly curved surfaceThis question was posed to me in an online quiz.I need to ask this question from Development of Surfaces topic in portion Development of Surfaces, Isometric Projections, Perspective Projections & Transformation of Projections of Civil Engineering Drawing

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Correct choice is (d) doubly curved surface

Easiest EXPLANATION: Double-curved SURFACES, such as a sphere do not produce true developments, because they do not CONTAIN any straight LINES.
Discussion