Answer
$\dfrac{x^2}{16}-\dfrac{y^2}{64}=1$
With horizontal traverse axis.
Work Step by Step
Endpoints: $(-4,0), (4, 0)$ and Asymptote: $ y=2x $
We are given that $ a=4$
Since $\dfrac{b}{a}=2 \implies b=8$
so, $ b^2=64$
Thus, the equation for hyperbola is:
$\dfrac{x^2}{16}-\dfrac{y^2}{64}=1$
And the traverse axis is horizontal.
