Problem

Figure 2 shows a sketch of the curve with equation

$$y^2=2x^2+15x+10y$$

(a) Find

$$\frac{dy}{dx}$$

in terms of $x$ and $y$.

The curve is not defined for values of $x$ in the interval $(p,q)$, as shown in Figure 2.

(b) Using your answer to part (a) or otherwise, find the value of $p$ and the value of $q$.

(Solutions relying entirely on calculator technology are not acceptable.)