Differentia geometry past/Previous question paper
(a) Define the rectifying plane?
Prove that the normal plane at any point to the locus of center of curvature any cur bisect curvature at the corresponding the original
(a). Define involutes and evolutes ? (b). Prove that there exist an infinite family of evolutes for space curve (involutes)? (10)
a). Define characteristics and envelope of a family? (b). Prove that the envelope of one parameter family of the surfaces touch each member the family each point of chracteristics? (10)
(a). Find the envelope of the plane ix+my+nz=p: Where p²= a21²+ b²m² + c²n² and a, b, c are constant? (b). Find whether xyz = a³ is developable (10)
curvature of indicatrix of normal? (b). Prove that the edge of regression of the tangent developable the curve itself? (10)