Which of the following equations ( t being the parameter ) can't represent a hyperbola

Eliminating t.

By Solving given equations, in 1^st point we have

$x=a\left(\frac{1-t^2}{1+t^2}\right),y=b\left(\frac{2t}{1+t^2}\right)$

If $t=\tan \theta$  then $\frac{x}{a}=\cos 2\theta ,\frac{y}{5}=\sin 2\theta$

$\Rightarrow \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$  is an ellipse, not the hyperbola