Let p be a point on m with gaussian curvature k at p then (a) if k0, the dupin indicatrix is an ellipse; (b) if k 0, the dupin indicatrix is two conjugate pairs of hyperbolas; and (c) if k 0, the dupin indicatrix is two parallel lines if one principal curvature is not zero and is empty if both principal curvatures are zero

During the experiment if you could triple the breakaway magnetic force with all other quantities left unchanged, what is the new value for the critical velocity if it was v0 (initial velocity), initially? (b) now if you halved the radius with all other quantities left unchanged, what is the new critical velocity if it was v0 (initial velocity), initially? (c) if during the experiment, critical velocity quadrupled with all other quantities left unchanged, what is the new breakaway force if its magnitude was initially f0,?