Question

How do you write the equation of the hyperbola given Foci: (-sqrt34,0),(sqrt34,0) and vertices (-5,0), (5,0)?

Answer 1

The equation of the hyperbola is `x^2/25-y^2/9=1`

Explanation:

The equation of a hyperbola is `(x-h)^2/a^2-(y-k)^2/b^2=1`

This a left to right hyperbola
The center is `(0,0)` that is `h=k=0`
Therefore `a=5`
And as the foci are `(h+-c,k)=+-sqrt34,0`
So `c=sqrt(a^2+b^2)`

Therefore, `c^2=a^2+b^2`
`b^2=c^2-a^2=34-25=9`
So `b=3`
So the equation of the hyperbola is `x^2/25-y^2/9=1`

graph{x^2/25-y^2/9=1 [-20, 20, -10, 10]}