17003

3 D 10670

18. Prove that affine transformations maps ellipses to ellipses, parabolas to parabolas and hyperbolas
to hyperbolas.

19. Determine the point of Rp? at which the line through the points[1, 2, - 3] and [2,—1,0] meetsthe
line through the points [1, 0, - 1] and (1, 1, 1].
(5 x 5 = 25 marks)

Section C

Answer any one question.
The question carries 11 marks.

20. Prove that the conic E with equation 92 _ 10xy + By? + 14x —2y +3=0 is ahyperbola. Determine
its centre, and its major and minor axes.
21. State and prove Ceva’s theorem.

(1 x 11 = 11 marks)

17003