(a) Identify and trace the conicoid  Describe its sections by the planes 

(a) Find the equations of the line through (1,3, 4 ) and parallel to the line joining the  points (−4, 5, 3) and (8, 9, 7).

(d) Find the equation of the cylinder with base 

(b) (i) Show that  represents the equation of a line passing  through (2, 3) and (−4, 7).

(ii) Prove that the equation of a line through  and  can be 

expressed in the form  

(c) Show that the conicoid  is central. Hence find its centre. 

(b) Transform the equation   by shifting the origin to (1, 2, 0) without changing the directions of the coordinate axes. What object does this new equation represent? Give a rough sketch of it. 

(a) Examine which of the following conicoids are central and which are non-central. Also determine which of the central conicoids have centre at the origin. 

(i)  

(ii)  

(iii)