Question

How do you write the equation of the hyperbola given Foci: (-8,0),(80) and vertices (-7,0), (7,0)?

Answer 1

The equation of the ellipse is `x^2/49-y^2/15=1`

Explanation:

The center is `=(0,0)`
The vertices are `=(+-a,0)=(+-7,0)`
The foci are `=+-c,0`
Therefore, `c^2=a^2+b^2`
So, `b^2=c^2-a^2=64-49=15`

The equation of the hyperbola is
`x^2/a^2-y^2/b^2=1`

`x^2/49-y^2/15=1`
graph{x^2/49-y^2/15=1 [-16.02, 16.02, -8.01, 8.02]}