Question

What is the relation between evolutes and envelopes?

(a) Evolutes and envelopes are same

(b) Evolute is the envelope of normals to a curve

(c) Evolute is the envelope of tangents to a curve

(d) Envelope is the evolute of normal to a curve

I have been asked this question in an interview for job.

I would like to ask this question from Envelopes in division Differential Calculus of Engineering Mathematics

Answer 1

Right option is (b) Evolute is the envelope of normals to a curve

To elaborate: Evolute is the locus of the all the centres of curvature of the curve whereas envelope is the curve which touches all the members of the family of the curve i.e Envelope is tangent to all the curves in a family of curves. Hence, evolute is the envelope of normal to a curve.