Find the equation of a line which passes through $$\left(2 \cos ^3(\theta), 2 \sin ^3(\theta)\right)$$ and is perpendicular to the line $$x \cos (\theta)-y \sin (\theta)=2 \cos (2 \theta)$$.

The value of $$p$$ for which the equation $$x^2+p x y+y^2-5 x-7 y+6=0$$ represents a pair of straight lines is

If one of the line represented by $$-a x^2+2 h x y+b y^2=0$$ passes through $$(2,3)$$ and the other passes through $$(4,5)$$, then $$a+2 h+b$$ equals

If the lines represented by the equation $$2 x^2-p x y+2 y^2=0$$ are real, then the value of $$p$$ lies in the interval