C4 vectors question 15

If you find $dy/dx$ you should get $\displaystyle \frac{dy}{dx}=\frac{g'(\theta)}{f'(\theta)}$.

So the direction of the vector of the equation that has gradient $\frac{g'(\theta)}{f'(\theta)}$
is $\begin{pmatrix} f'(\theta) \\ g'(\theta) \end{pmatrix}$.

Think of it this way if a line has a gradient of 4 then the vector that represent sthe direction of the line is $\begin{pmatrix} 1 \\ 4 \end{pmatrix}$.

Then just apply this general direction to find the direction vectors of the curves defined below.