For $$\alpha \in\left[0, \frac{\pi}{2}\right]$$, the angle between the lines represented by $$[x \cos \theta-y] [(\cos \theta+\tan \alpha) x-(1-\cos \theta \tan \alpha) y]=0$$ is

The point to which the origin should be shifted in order to eliminate the $$x$$ and $$y$$ terms from the equation $$9 x^2+4 y^2+10 x+12 y+1=0$$ is

If $$A(1,3)$$ and $$C(7,5)$$ are two opposite vertices of a square, then find the equation of a side passing through $$A$$.

$$C$$ is the centroid of the triangle with vertices $$(3,-1),(1,3)$$ and $$(2,4)$$. Let $$P$$ be the point of intersection of the lines $$x+3 y-1=0$$ and $$3 x-y+1=0$$. Then a line which passes through both points $$C$$ and $$P$$ would also passes through the point .......