1.5: Past-paper question 7

4PM1/2R/June/2024 — Question 7 · 14 marks

1.5 diagram 1
Figure 2 shows a sketch of part of the curve CC with equation
y=x214x+5wherex54y = \frac{x^2 - 1}{4x + 5} \quad \mathrm{where} x \neq -\frac{5}{4}
(a) Write down the equation of the asymptote to CC that is parallel to the yy-axis.
(1)
The line ll is the normal to CC at the point where x=1x = -1
(b) Find an equation of ll
(7)
The line ll meets CC again at the point DD
(c) Find the coordinates of DD
(6)