Connect a derivative discriminant to the missing range

· Techniques of Differentiation

$C:y=(x^2+a)/(x-a)$, x≠a, where a is a non-zero constant.

(i) Given the oblique asymptote y=x+2, find a.1 mark

(ii) Find the set of values of a if C has two turning points.3 marks

(iii) Using a from (i) and an algebraic method, show C cannot exist for y₁<y<y₂, determining y₁,y₂ exactly.3 marks

(iv) Hence sketch C, clearly showing the asymptotes and stationary-point coordinates.3 marks