The diagram shows the curve $C$ passes through the point $A(a+1, 12)$ and has an asymptote with

Question

The diagram shows the curve $C$ passes through the point $A(a+1, 12)$ and has an asymptote with equation $x = 4$. It is also given that $C$ has a gradient function $\frac{1}{x-a}$, where $x > a$. Show that $a = 4$. Hence find the equation of $C$.[3] Use a non-calculator method to find the equation of the tangent to $C$ at the point $A$.[1] Hence find the area of the finite region bounded by the curve $C$, the tangent found in part (b) and the $x$-axis.[4]

Accepted Answer

(a)$y= ln (x-4)+12$ (b)$y=x+7$ (c)61.0 units$^2$

2024 DHS H1 Q2

2024 DHS H1 Q2