(a) The candidates’ poor knowledge of coordinate geometry was evident in this question. The equation 2x2 + 2y2 + 10x + ky – 13 = 0 is equivalent to x2 + y2 + 5x + k/2y - 13/2 = 0
which when compared with x2 + y2 + 2gx + 2fy + c = 0
gives g = 5/2, f = k/4 and c = - 13/2. Recalling that r2 = g2 + f2 – c, we have
25 = 25/4 + k2/16 + 13/2 which gives k = 14.
(b) Most candidates could not use determinant method to solve the given equations. Hence many scored zero for using another method other than determinant method.
