Answer
$\dfrac{y^{2}}{4}-\dfrac{x^{2}}{21}=1$; equation of a hyperbola.
Work Step by Step
From the given points, we have $a=2$ and $c=5$
Thus, $c^2=a^2+b^2$ or, $5^2=2^2+b^2$
$b^2=25-4=21$
Hence, $\dfrac{y^{2}}{4}-\dfrac{x^{2}}{21}=1$; equation of a hyperbola.
