The coordinates of the point p on the curve $\mathrm{x}=\mathrm{a}\left(\mathrm{\theta }+\sin \mathrm{\theta }\right),\mathrm{y}=\mathrm{a}(1-\mathrm{cos\theta })$ where the tangent is inclined at an angle $\frac{\mathrm{\pi }}{4}$ to the x - axis, are

$$\begin{gathered} \mathrm{x}=\mathrm{a}\left(\mathrm{\theta }+\sin \mathrm{\theta }\right) , \mathrm{y}=\mathrm{a}(1-\mathrm{cos\theta }) \\ \frac{dx}{d\mathrm{\theta }}=\mathrm{a}(1+\mathrm{cos\theta }) , \frac{dy}{d\mathrm{\theta }}=a\left(\mathrm{sin\theta }\right) \end{gathered}$$

$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{a} \sin \mathrm{\theta }}{\mathrm{a}(1+\cos \mathrm{\theta })}$Tangent is inclined at an angle $\frac{\mathrm{\pi }}{4}$ so  $\mathrm{\theta }=\frac{\mathrm{\pi }}{2}$ on solving 
$\therefore \mathrm{point} \left(\mathrm{a}\left(\frac{\mathrm{\pi }}{2}+1\right),\mathrm{a}\right)$