1.17: Past-paper question 7

Figure 2 shows a sketch of part of the curve $\displaystyle C$ with equation

(a) Write down the equation of the asymptote to $\displaystyle C$ that is parallel to the $\displaystyle y$-axis.

The line $\displaystyle l$ is the normal to $\displaystyle C$ at the point where $\displaystyle x = -1$

(b) Find an equation of $\displaystyle l$

The line $\displaystyle l$ meets $\displaystyle C$ again at the point $\displaystyle D$

(c) Find the coordinates of $\displaystyle D$