Question 1 (10 marks) a. Find a parametric equation for the line containing the points (1, -3, 4) and (3, -4, 5). ( 2 marks) Consider the curve given by the following relation: 169x2 1144};2 : 24336 i. Classify the curve. (I mark) ii. Determine all important features such as vertices, foci, asymptotes etc. where present. (2 marks) iii. Sketch the curve, clearly labelling the features from the previous part. You may use software to help with the sketch. (1 mark) Consider the the function f(x,y)=2lxllyl i. On a single set of xyaxes, draw contours f (x, y) : k for k : 0, 1 and 2. The contours must be clearly labelled with the corresponding value of 1:. You may use software to help. ( 3 marks) ii. Briey describe the surface dened by : : f(x, y) . Note that this is not a simple conic or quartic so you will need to qualitatively describe the general shape of the surface in a sentence or two. (I mark)