Question

Write the equation of a hyperbola with vertices at (-4, 0) and (4, 0) and co-vertices (0, 5) and (0, -5).

Answer 1

The answer to your question is
`(x^(2))/(16) - (y^(2) )/(25) = 1`

Explanation:

Data

(-4, 0) (4, 0)

(0, 5) (0, -5)

Plot the point to determine if it is a horizontal or vertical hyperbola

It is a horizontal hyperbola because the vertices are in a horizontal line. The center is (0, 0).

a = 4

b = 5

Formula

`(x^(2) )/(a^(2)) - (y^(2))/(b^(2)) = 1`

Substitution

`(x^(2))/(4^(2)) - (y^(2))/(5^(2)) = 1`

Equation

`(x^(2))/(16) - (y^(2))/(25) = 1`