Question

Find the equation of the hyperbola centered at the origin that satisfies the given conditions x-intercept

1. The hyperbola centered at the origin’s equation that complies with the requirements is x²/9 – y²/25 = 1.
The hyperbola has a horizontal transverse axis because it has x-intercepts.
The equation for a hyperbola with a horizontal transverse axis has the following standard form:
(x – h)²/a² – (y – k)²/b² = 1.
There is a center at (h,k).
The vertices are separated by a distance of 2a.
a and b have values of;
2a = x₂ – x₁ = 3 – (-3) = 3 + 3 = 6 for “a,” and a = 6/2 = 3 and b = 5.
The hyperbola’s equation, with its center at the origin, that meets the requirements is;
(x – h)²/a² – (y – k)²/b² = 1,
or, (x – 0)²/3² – (y – 0)²/5² = 1,
or, x²/9 – y²/25 = 1.
As a result, the hyperbola’s equation, centered at its origin, that fulfills the requirements is x²/9 – y²/25 = 1.