Let the variable line y = kx + h is tangent to the hyperbola x^ 2 4...

Equation of the tangent $y = kx + h$ is compared with $y = mx \pm \sqrt{4m^{2} - 9}$
$⇒ 1 = \dfrac{m}{k} = \dfrac{\pm \sqrt{4m^{2} - 9}}{h}$
i.e. $m = k$ and $h = \sqrt{4m^{2} - 9}$
$⇒ h = \sqrt{4k^{2} - 9}$
$⇒ 4y^{2} - x^{2} = 9$
⇒ \dfrac{{\text{y}^{2}}{{\left(\dfrac{3}{2}\right)}^{2}} - \dfrac{{\text{x}^{2}}{{3}^{2}} = 1
⇒ {3}^{2} = {\left(\dfrac{3}{2}\right)}^{2} \left({\text{e}^{2} -1\right)
$⇒ e^{2} = 5 ⇒ e = \sqrt{5}$> 1$</p><p>Hence, the conic is not an ellipse</p>$