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Recover the coefficients from a vertical and an oblique asymptote

C1C_1 has equation y=(ax2+bx)/(x+c)y=(ax^2+bx)/(x+c).

(i) It has vertical asymptote x=2 and an oblique asymptote through (0,10) and (−2,0). Find a,b,c.

(ii) Hence sketch C1C_1, clearly stating all asymptotes and stationary points.

[2014/NJC/MYE/7(part)]

CJC · Discussion · Question 4

The oblique line’s slope is a, but its intercept is b+2 a.

Read the worked solution