Question:

Number of correct statements is $k$. Then $2k$ is: I) Chord joining $P(at_1^2,2at_1)$ and $Q(at_2^2,2at_2)$ on $y^2=4ax$ passes through focus when $t_1t_2=-1$ and focal chord PQ $=|a|(t_1+1/t_1)^2\ge 4a$. II) $P=\{\theta:\sin\theta-\cos\theta=\sqrt{2}\cos\theta\}$ and $Q=\{\theta:\sin\theta+\cos\theta=\sqrt{2}\sin\theta\}$, then $P=Q$. III) If $a,b,c,d$ distinct nonzero reals: $(a^2+b^2+c^2)p^2-2(ab+bc+cd)p+(b^2+c^2+d^2)\le 0$, then $a,b,c,d$ are in GP.