determine the standard form of the equation of a hyperbola with vertices (plus of minus 2, 0) and passing through (4,3).

Expert Answers
rcmath eNotes educator| Certified Educator

Since vertices are (-2,0) and (2,0), this means the hyperbola is centered at (0,0) and a=2. 

So far we have `x^2/4-y^2/b=1`

To find b^2, we will plug in the additional point.

`4^2/4-3^2/b^2=1=>`

`4-9/b^2=1=>`

`-9/b^2=-3=>`

`3=b^2`

Hence the equation is `x^2/4-y^2/3=1`