3.5.4 Surfaces of the 2-nd order

Problem: Let the given surface be \( \sigma: 9(x-1)^{2}+4 y^{2}-36 z^{2}=36 \) and the points be \( M_{1}(1 ; 0 ; 0), M_{2}(3 ; 1 ; 1) \). 1) Define the type of the surface \( \sigma \), 2) Draw the surface \( \sigma \), 3) Find sections of the surface \( \sigma \) with coordinate planes and define their foci and asymptotes, 4) Define the location of the points \( M_{1} \) and \( M_{2} \) in relation to the surface \( \sigma \) 5) Find the points of intersection of the straight line passing through points \( M_{1} \) and \( M_{2} \) with the surface \( \sigma \).