Find an equation for the hyperbola that has its center at the origin and satisfies the given conditions.

Question

vertices V(±4, 0),    asymptotes y = ±2x

Answer 1

Given the distance from the vertex to the center is 4, if the asymptotes is y =+/-x, the hyerbola equation is

x^2 - y^2 = +/- 16 (a 45 degree rotation of y = +/- 8/x)

When aysymptotes slope increases to 2 (i.e. y = +/- 2x), the y value will be stretched by a factor of 2. So replace y with y/2 in the above equation:

The answer is x^2 - y^2 / 4 = +/-16.