Target Mathematics

1.31: Reciprocal curves and asymptotes

4PM1/1/January/2017 — Question 6 · 6 marks

1.31 diagram 1
Figure 3 shows a sketch of the curve with equation
y=bx+cx+a,x≠−ay=\frac{bx+c}{x+a},\qquad x\ne-a
where aa, bb and cc are integers.
The equations of the asymptotes to the curve are x=−2x=-2 and y=3y=3.
The curve crosses the yy-axis at (0,3.5)(0,3.5).
(a) Write down the value of aa and the value of bb. (2)
(b) Find the value of cc. (2)
Given that the curve crosses the xx-axis at (s,0)(s,0)
(c) find the value of ss. (2)