Which is the equation of a hyperbola centered at the origin with x-intercept +\- 3 and asymptote y=2x

Step-by-step explanation:

The hyperbola has x-intercepts, so it has a horizontal transverse axis.

The standard form of the equation of a hyperbola with a horizontal transverse axis is  

The center is at (h,k).

The distance between the vertices is 2a.

The equations of the asymptotes are

1. Calculate h and k. The hyperbola is symmetric about the origin, so  

h = 0 and k = 0

2. For 'a': 2a = x₂ - x₁ = 3 - (-3) = 3 + 3 = 6

a = 6/2 = 3  

3. For 'b': The equation for the asymptote with the positive slope is  

Thus,  asymptote has the slope of

4.  The equation of the hyperbola is

The attachment below represents your hyperbola with x-intercepts at ±3 and asymptotes with slope ±2.

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are

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step-by-step explanation: