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

do you have a formula possibly

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)