Find the standard form of the equation of the hyperbola with the given characteristics. Vertices: (±4, 0); foci: (±5, 0)

Question

Find the standard form of the equation of the hyperbola with the given characteristics.

Vertices: (±4, 0); foci: (±5, 0)

Answer 1

x^2/16 - y^2/9 = 1

or

9x^2 -16y^2 = 144

x^2/a^2 - y^2/b^2 = 1

where c^2=a^2 +b^2

(+/-c,0) = foci= (+/-5,0)

(+/-a,0) = vertices (+/-4,0)

b^2 = c^2-a^2 = 25-16 = 9

b =+/-sqr9 = +/-3

x^2/4^2-y^2/3^2=1