A straight line passes through (4, 5) and makes an angle 60º with x-axis in the positive direction. Its equation in the parametric form

$$\begin{gathered} Let \left(4 ,5 \right)=\left(x_1 , y_1\right) and \theta ={60}^{°} \\ \therefore The parametric equations are x=x_1+r \cos \theta , y=y_1+r \sin \theta \\ \Rightarrow x=4+r \cos 60 ,y=5+r \sin 60 \\ \Rightarrow x=4+r\left(\frac{1}{2}\right) , y=5+r \left(\frac{\sqrt{3}}{2}\right) ( let \lambda =\frac{1}{2} ) \\ \Rightarrow x=4+\lambda , y=5+\sqrt{3}\lambda \end{gathered}$$