The locus of a point $\mathrm{P}$ which divides the line joining $\left(1,\mathrm{ }0\right)$ and $\left(2\mathrm{ }\cos \mathrm{\theta },\mathrm{ }2\sin \mathrm{\theta }\right)$ internally in the ratio $2\mathrm{ }:\mathrm{ }3$ for all $\mathrm{\theta }$ , is a

Statement (i): The points $\left(-1,0\right),\left(4,-2\right)$ and $\left(\cos 2\theta ,\sin 2\theta \right)$ are collinear

Statement (ii): The points $\left(-1,0\right),\left(4,-2\right)$ and $\left(\frac{1-{\tan }^2\theta }{1+{\tan }^2\theta },\frac{2\tan \theta }{1+{\tan }^2\theta }\right)$ are collinear