Q1: The properties of autogenous curve for automobiles are given by

ANS:C - Bernoulli's Lemniscate

Bernoulli's Lemniscate is a type of curve named after the mathematician Jacob Bernoulli. It has a characteristic shape resembling a figure-eight. Imagine two fixed points in space called foci, and Bernoulli's Lemniscate is the set of all points where the product of distances from these two foci remains constant. Visually, it looks like a loop that intersects itself at the midpoint between the foci. While it doesn't have immediate practical applications in engineering, it is studied for its mathematical properties and appears in various fields including physics and mathematics.