The angle between the lines represented by $$\cos \theta(\cos \theta+1) x^2-\left(2 \cos \theta+\sin ^2 \theta\right) x y+(1-\cos \theta) y^2=0$$ is

If the axes are rotated through an angle $$45 \Upsilon$$, the coordinates of the point $$(2 \sqrt{2},-3 \sqrt{2})$$ in the new system are

the sum of the squares of the intercepts made the line $$5x-2y=10$$ on the coordinate axes equals

For three consecutive odd integers $$a \cdot b$$ and $$c$$, if the variable line $$a x+b y+c=0$$ always passes through the point $$(\alpha, \beta)$$, the value of $$\alpha^2+\beta^2$$ equals