JEE Math Practice Question

Let $$C$$ be the centre of the circle $$x^{2}+y^{2}-x+2 y=\frac{11}{4}$$ and $$P$$ be a point on the circle. A line passes through the point $$\mathrm{C}$$, makes an angle of $$\frac{\pi}{4}$$ with the line $$\mathrm{CP}$$ and intersects the circle at the points $$Q$$ and $$R$$. Then the area of the triangle $$P Q R$$ (in unit $$^{2}$$ ) is :

1. A.2
2. B.2$$\sqrt2$$
3. C.$$8 \sin \left(\frac{\pi}{8}\right)$$
4. D.$$8 \cos \left(\frac{\pi}{8}\right)$$