Proving the equation of pair of lines is $x^2+2xy\sec(2\alpha)+y^2$ Prove that the equation of the pair of lines having an angle $\alpha$ with $x+y=0$ and passing through origin is $x^2+2xy\sec(2\alpha)+y^2=0$  I think we have to use rotation matrix but can't think of any concrete step to solve it.

Hint: Let $u=(x,y), v=(1,-1)$ and note that the angle condition means that $u\cdot v= \vert\vert u \vert\vert \cdot \vert\vert v \vert\vert \cos \alpha$
