Answer
$\dfrac{x^{2}}{9}-\dfrac{y^{2}}{36}=1$; equation of hyperbola.
Work Step by Step
From the given points we have $a=3$
and
Asymptotes : $y=\pm2x$ this implies that $\frac{b}{a}=2$
Put $a=3$ thus, $\frac{b}{3}=2$ or $b=6$
or, $a^2=9, b^2=36$
Hence,$\dfrac{x^{2}}{9}-\dfrac{y^{2}}{36}=1$; equation of hyperbola.
